ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Constructions Ex 16.1

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Constructions Ex 16.1

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Constructions Ex 16.1

Question 1.
Use a ruler and compass only in this question.
(i) Draw a circle, centre O and radius 4 cm.
(ii) Mark a point P such that OP = 7 cm.
Construct the two tangents to the circle from P. Measure and record the length of one of the tangents.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Constructions Ex 16.1

Question 2.
Draw a line AB = 6 cm. Construct a circle with AB as diameter. Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure the length of each tangent
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Constructions Ex 16.1

Question 3.
Construct a tangent to a circle of radius 4cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Constructions Ex 16.1

Question 4.
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Constructions Ex 16.1

Question 5.
Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Constructions Ex 16.1

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 1.
(a) In the figure (i) given below, triangle ABC is equilateral. Find ∠BDC and ∠BEC.
(b) In the figure (ii) given below, AB is a diameter of a circle with centre O. OD is perpendicular to AB and C is a point on the arc DB. Find ∠BAD and ∠ACD
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 2.
(a) In the figure given below, AB is a diameter of the circle. If AE = BE and ∠ADC = 118°, find
(i) ∠BDC (ii) ∠CAE.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
(b) In the figure given below, AB is the diameter of the semi-circle ABCDE with centre O. If AE = ED and ∠BCD = 140°, find ∠AED and ∠EBD. Also, Prove that OE is parallel to BD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 3.
(a) In the figure (i) given below, O is the centre of the circle. Prove that ∠AOC = 2 (∠ACB + ∠BAC).
(b) In the figure (ii) given below, O is the centre of the circle. Prove that x + y = z.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 4.
(a) In the figure (i) given below, AB is the diameter of a circle. If DC is parallel to AB and ∠CAB = 25°, find:
(i)∠ADC
(ii) ∠DAC.
(b) In the figure (ii) given below, the centre O of the smaller circle lies on the circumference of the bigger circle. If ∠APB = 70° and ∠BCD = 60°, find:
(i) ∠AOB
(ii) ∠ACB
(iii) ∠ABD
(iv) ∠ADB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 5.
(a) In the figure (i) given below, ABCD is a cyclic quadrilateral. If AB = CD, Prove that AD = BC.
(b) In the figure (ii) given below, ABC is an isosceles triangle with AB = AC. If ∠ABC = 50°, find ∠BDC and ∠BEC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 6.
A point P is 13 cm from the centre of a circle. The length of the tangent drawn from P to the circle is 12 cm. Find the distance of P from the nearest point of the circle.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 7.
Two circles touch each other internally. Prove that the tangents drawn to the two circles from any point on the common tangent are equal in length.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 8.
From a point outside a circle, with centre O, tangents PA and PB are drawn. Prove that
(i) ∠AOP = ∠BOP.
(ii) OP is the perpendicular bisector of the chord AB.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 9.
(a) The figure given below shows two circles with centres A, B and a transverse common tangent to these circles meet the straight line AB in C. Prove that:
AP : BQ = PC : CQ.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
(b) In the figure (ii) given below, PQ is a tangent to the circle with centre O and AB is a diameter of the circle. If QA is parallel to PO, prove that PB is tangent to the circle.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 10.
In the figure given below, two circles with centres A and B touch externally. PM is a tangent to the circle with centre A and QN is a tangent to the circle with centre B. If PM = 15 cm, QN = 12 cm, PA = 17 cm and QB = 13 cm, then find the distance between the centres A and B of the circles.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 11.
Two chords AB, CD of a circle intersect externally at a point P. If PB = 7 cm, AB = 9 cm and PD = 6 cm, find CD.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 12.
(a) In the figure (i) given below, chord AB and diameter CD of a circle with centre O meet at P. PT is tangent to the circle at T. If AP = 16 cm, AB = 12 cm and DP = 2 cm, find the length of PT and the radius of the circle
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
(b) In the figure (ii) given below, chord AB and diameter CD of a circle meet at P. If AB = 8 cm, BP = 6 cm and PD = 4 cm, find the radius of the circle. Also, find the length of the tangent drawn from P to the circle.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 13.
In the figure given below, chord AB and diameter PQ of a circle with centre O meet at X. If BX = 5 cm, OX = 10 cm and.the radius of the circle is 6 cm, compute the length of AB. Also, find the length of tangent drawn from X to the circle.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 14.
(a) In the figure (i) given below, ∠CBP = 40°, ∠CPB = q° and ∠DAB = p°. Obtain an equation connecting p and q. If AC and BD meet at Q so that ∠AQD = 2 q° and the points C, P, B and Q are concyclic, find the values of p and q.
(b) In the figure (ii) given below, AC is a diameter of the circle with centre O. If CD || BE, ∠AOB = 130° and ∠ACE = 20°, find:
(i)∠BEC
(ii) ∠ACB
(iii) ∠BCD
(iv) ∠CED.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 15.
(a) In the figure (i) given below, APC, AQB and BPD are straight lines.
(i) Prove that ∠ADB + ∠ACB = 180°.
(ii) If a circle can be drawn through A, B, C and D, Prove that it has AB as a diameter
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
(b) In the figure (ii) given below, AQB is a straight line. Sides AC and BC of ∆ABC cut the circles at E and D respectively. Prove that the points C, E, P and D are concyclic.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 16.
(a) In the figure (i) given below, chords AB, BC and CD of a circle with centre O are equal. If ∠BCD = 120°, find
(i) ∠BDC
(ii) ∠BEC
(iii) ∠AEC
(iv) ∠AOB.
Hence Prove that AOAB is equilateral.
(b) In the figure (ii) given below, AB is a diameter of a circle with centre O. The chord BC of the circle is parallel to the radius OD and the lines OC and BD meet at E. Prove that
(i) ∠CED = 3 ∠CBD
(ii) CD = DA.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

Question 17.
(a) In the adjoining figure, (i) given below AB and XY are diameters of a circle with centre O. If ∠APX = 30°, find
(i) ∠AOX
(ii) ∠APY
(iii) ∠BPY
(iv) ∠OAX.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
(b) In the figure (ii) given below, AP and BP are tangents to the circle with centre O. If ∠CBP = 25° and ∠CAP = 40°, find :
(i) ∠ADB
(ii) ∠AOB
(iii) ∠ACB
(iv) ∠APB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 1.
In the given figure, O is the centre of the circle. If ∠ABC = 20°, then ∠AOC is equal to
(a) 20°
(b) 40°
(c) 60°
(d) 10°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 2.
In the given figure, AB is a diameter of the circle. If AC = BC, then ∠CAB is equal to
(a) 30°
(b) 60°
(c) 90°
(d) 45°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 3.
In the given figure, if ∠DAB = 60° and ∠ABD = 50° then ∠ACB is equal to
(a) 60°
(b) 50°
(c) 70°
(d) 80°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 4.
In the given figure, O is the centre of the circle. If ∠OAB = 40°, then ∠ACB is equal to
(a) 50°
(b) 40°
(c) 60°
(d) 70°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 5.
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140°, then ∠BAC is equal to
(a) 80°
(b) 50°
(c) 40°
(d) 30°
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 6.
In the given figure, O is the centre of the circle. If ∠BAO = 60°, then ∠ADC is equal to
(a) 30°
(b) 45°
(c) 60°
(d) 120°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 7.
In the given figure, O is the centre of the circle. If ∠AOB = 90° and ∠ABC = 30°, then ∠CAO is equal to
(a) 30°
(b) 45°
(c) 90°
(d) 60°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 8.
In the given figure, O is the centre of a circle. If the length of chord PQ is equal to the radius of the circle, then ∠PRQ is
(a) 60°
(b) 45°
(c) 30°
(d) 15°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 9.
In the given figure, if O is the centre of the circle then the value of x is
(a) 18°
(b) 20°
(c) 24°
(d) 36°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 10.
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is
(a) 7 cm
(b) 12 cm
(c) 15 cm
(d) 24.5 cm
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 11.
From a point which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is
(a) 60 cm²
(b) 65 cm²
(c) 30 cm²
(d) 32.5 cm²
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 12.
If the angle between two radii of a circle is 130°, the angle between the tangents at the ends of the radii is
(a) 90°
(b) 50°
(c) 70°
(d) 40°
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 13.
In the given figure, PQ and PR are tangents from P to a circle with centre O. If ∠POR = 55°, then ∠QPR is
(a) 35°
(b) 55°
(c) 70°
(d) 80°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 14.
If tangents PA and PB from an exterior point P to a circle with centre O are inclined to each other at an angle of 80°, then ∠POA is equal to
(a) 50°
(b) 60°
(c) 70°
(d) 100°
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 15.
In the given figure, PA and PB are tangents from point P to a circle with centre O. If the radius of the circle is 5 cm and PA ⊥ PB, then the length OP is equal to
(a) 5 cm
(b) 10 cm
(c) 7.5 cm
(d) 5√2 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 16.
At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is
(a) 4 cm
(b) 5 cm
(c) 6 cm
(d) 8 cm
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 17.
If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other is
(a) 3 cm
(b) 6 cm
(c) 9 cm
(d) 1 cm
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 18.
In the given figure, AB is a chord of the circle such that ∠ACB = 50°. If AT is tangent to the circle at the point A, then ∠BAT is equal to
(a) 65°
(b) 60°
(c) 50°
(d) 40°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 19.
In the given figure, O is the centre of a circle and PQ is a chord. If the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is
(a) 100°
(b) 80°
(c) 90°
(d) 75°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 20.
In the given figure, PA and PB are tangents to a circle with centre O. If ∠APB = 50°, then ∠OAB is equal to
(a) 25°
(b) 30°
(c) 40°
(d) 50°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 21.
In the given figure, sides BC, CA and AB of ∆ABC touch a circle at point D, E and F respectively. If BD = 4 cm, DC = 3 cm and CA = 8 cm, then the length of side AB is
(a) 12 cm
(b) 11 cm
(c) 10 cm
(d) 9 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 22.
In the given figure, sides BC, CA and AB of ∆ABC touch a circle at the points P, Q and R respectively. If PC = 5 cm, AR = 4 cm and RB = 6 cm, then the perimeter of ∆ABC is
(a) 60 cm
(b) 45 cm
(c) 30 cm
(d) 15 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 23.
PQ is a tangent to a circle at point P. Centre of a circle is O. If ∆OPQ is an isosceles triangle, then ∠QOP is equal to
(a) 30°
(b) 60°
(c) 45°
(d) 90°
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 24.
In the given figure, PT is a tangent at T to the circle with centre O. If ∠TPO = 25°, then the value of x is
(a) 25°
(b) 65°
(c) 115°
(d) 90°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 25.
In the given figure, PA and PB are tangents at points A and B respectively to a circle with centre O. If C is a point on the circle and ∠APB = 40°, then ∠ACB is equal to
(a) 80°
(b) 70°
(c) 90°
(d) 140°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 26.
In the given figure, two circles touch each other at A. BC and AP are common tangents to these circles. If BP = 3.8 cm, then the length of BC is equal to
(a) 7.6 cm
(b) 1.9 cm
(c) 11.4 cm
(d) 5.7 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 27.
In the given figure, if sides PQ, QR, RS and SP of a quadrilateral PQRS touch a circle at points A, B, C and D respectively, then PD + BQ is equal to
(a) PQ
(b) QR
(c) PS
(d) SR
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 28.
In the given figure, PQR is a tangent at Q to a circle. If AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to
(a) 20°
(b) 40°
(b) 35°
(d) 45°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

Question 29.
Two chords AB and CD of a circle intersect externally at a point P. If PC = 15 cm, CD = 7 cm and AP = 12 cm, then AB is
(a) 2 cm
(b) 4 cm
(c) 6 cm
(d) none of these
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles MCQS

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 1.
Find the length of the tangent drawn to a circle of radius 3 cm, from a point distant 5 cm from the centre.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

LearnCram.com also covered previous Year argumentative essay topics asked in ICSE board exams.

Question 2.
A point P is at a distance 13 cm from the centre C of a circle and PT is a tangent to the given circle. If PT = 12 cm, find the radius of the circle.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 3.
The tangent to a circle of radius 6 cm from an external point P, is of length 8 cm. Calculate the distance of P from the nearest point of the circle.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 4.
Two concentric circles are of the radii 13 cm and 5 cm. Find the length of the chord of the outer circle which touches the inner circle.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 5.
Two circles of radii 5 cm and 2-8 cm touch each other. Find the distance between their centres if they touch:
(i) externally
(ii) internally.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 6.
(a) In figure (i) given below, triangle ABC is circumscribed, find x.
(b) In figure (ii) given below, quadrilateral ABCD is circumscribed, find x.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 7.
(a) In figure (i) given below, quadrilateral ABCD is circumscribed; find the perimeter of quadrilateral ABCD.
(b) In figure (ii) given below, quadrilateral ABCD is circumscribed and AD ⊥ DC ; find x if radius of incircle is 10 cm.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 8.
(a) In the figure (i) given below, O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm, find the radius of the circle.
(b) In the figure (ii) given below, from an external point P, tangents PA and PB are drawn to a circle. CE is a tangent to the circle at D. If AP = 15 cm, find the perimeter of the triangle PEC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 9.
(a) If a, b, c are the sides of a right triangle where c is the hypotenuse, prove that the radius r of the circle which touches the sides of the triangle is given by
\(r= \frac { a+b-c }{ 2 } \)
(b) In the given figure, PB is a tangent to a circle with centre O at B. AB is a chord of length 24 cm at a distance of 5 cm from the centre. If the length of the tangent is 20 cm, find the length of OP.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 10.
Three circles of radii 2 cm, 3 cm and 4 cm touch each other externally. Find the perimeter of the triangle obtained on joining the centres of these circles.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 11.
(a) In the figure (i) given below, the sides of the quadrilateral touch the circle. Prove that AB + CD = BC + DA.
(b) In the figure (ii) given below, ABC is triangle with AB = 10cm, BC = 8cm and AC = 6cm (not drawn to scale). Three circles are drawn touching each other with vertices A, B and C as their centres. Find the radii of the three circles
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 12.
(a) ln the figure (i) PQ = 24 cm, QR = 7 cm and ∠PQR = 90°. Find the radius of the inscribed circle ∆PQR
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
(b) In the figure (ii) given below, two concentric circles with centre O are of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12cm, find BP.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 13.
(a) In the figure (i) given below, AB = 8 cm and M is mid-point of AB. Semi-circles are drawn on AB, AM and MB as diameters. A circle with centre C touches all three semi-circles as shown, find its radius.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
(b) In the figure (ii) given below, equal circles with centres O and O’ touch each other at X. OO’ is produced to meet a circle O’ at A. AC is tangent to the circle whose centre is O. O’D is perpendicular to AC. Find the value of :
(i) \(\\ \frac { AO’ }{ AO } \)
(ii) \(\frac { area\quad of\quad \Delta ADO’ }{ area\quad of\quad \Delta ACO } \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 14.
The length of the direct common tangent to two circles of radii 12 cm and 4 cm is 15 cm. Calculate the distance between their centres.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 15.
Calculate the length of a direct common tangent to two circles of radii 3 cm and 8 cm with their centres 13 cm apart.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 16.
In the given figure, AC is a transverse common tangent to two circles with centres P and Q and of radii 6 cm and 3 cm respectively. Given that AB = 8 cm, calculate PQ.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 17.
Two circles with centres A, B are of radii 6 cm and 3 cm respectively. If AB = 15 cm, find the length of a transverse common tangent to these circles.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 18.
(a) In the figure (i) given below, PA and PB are tangents at a points A and B respectively of a circle with centre O. Q and R are points on the circle. If ∠APB = 70°, find (i) ∠AOB (ii) ∠AQB (iii) ∠ARB
(b) In the figure (ii) given below, two circles touch internally at P from an external point Q on the common tangent at P, two tangents QA and QB are drawn to the two circles. Prove that QA = QB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 19.
In the given figure, AD is a diameter of a circle with centre O and AB is tangent at A. C is a point on the circle such that DC produced intersects the tangent af B. If ∠ABC = 50°, find ∠AOC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 20.
In the given figure, tangents PQ and PR are drawn from an external point P to a circle such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ, Find ∠RQS
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 21.
(a) In the figure (i) given below, PQ is a tangent to the circle at A, DB is a diameter, ∠ADB = 30° and ∠CBD = 60°, calculate (i) ∠QAB (ii) ∠PAD (iii) ∠CDB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
(b) In the figure (ii) given below, ABCD is a cyclic quadrilateral. The tangent to the circle at B meets DC produced at F. If ∠EAB = 85° and ∠BFC = 50°, find ∠CAB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 22.
(a) In the figure (i) given below, O is the centre of the circle and SP is a tangent. If ∠SRT = 65°, find the value of x, y and z. (2015)
(b) In the figure (ii) given below, O is the centre of the circle. PS and PT are tangents and ∠SPT = 84°. Calculate the sizes of the angles TOS and TQS.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 23.
In the given figure, O is the centre of the circle. Tangents to the circle at A and B meet at C. If ∠ACO = 30°, find
(i) ∠BCO (ii) ∠AOR (iii) ∠APB
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 24.
(a) In the figure (i) given below, O is the centre of the circle. The tangent at B and D meet at P. If AB is parallel to CD and ∠ ABC = 55°. find (i) ∠BOD (ii) ∠BPD
(b) In the figure (ii) given below. O is the centre of the circle. AB is a diameter, TPT’ is a tangent to the circle at P. If ∠BPT’ = 30°, calculate : (i) ∠APT (ii) ∠BOP.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 25.
In the adjoining figure, ABCD is a cyclic quadrilateral.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
The line PQ is the tangent to the circle at A. If ∠CAQ : ∠CAP = 1 : 2, AB bisects ∠CAQ and AD bisects ∠CAP, then find the measure of the angles of the cyclic quadrilateral. Also prove that BD is a diameter of the circle.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 26.
In a triangle, ABC, the incircle (centre O) touches BC, CA and AB at P, Q and R respectively. Calculate (i) ∠QOR (ii) ∠QPR given that ∠A = 60°.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 27.
(a) In figure (0 given below, AB is a diameter. The tangent at C meets AB produced at Q, ∠CAB = 34°. Find
(i) ∠CBA (ii) ∠CQA (2006)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
(b) In the figure (ii) given below, AP and BP are tangents to the circle with centre O. Given ∠APB = 60°, calculate.
(i) ∠AOB (ii) ∠OAB (iii) ∠ACB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 28.
(a) In the figure (i) given below, O is the centre of the circumcircle of triangle XYZ. Tangents at X and Y intersect at T. Given ∠XTY = 80° and ∠XOZ = 140°, calculate the value of ∠ZXY. (1994)
(b) In the figure (ii) given below, O is the centre of the circle and PT is the tangent to the circle at P. Given ∠QPT = 30°, calculate (i) ∠PRQ (ii) ∠POQ.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 29.
Two chords AB, CD of a circle intersect internally at a point P. If
(i) AP = cm, PB = 4 cm and PD = 3 cm, find PC.
(ii) AB = 12 cm, AP = 2 cm, PC = 5 cm, find PD.
(iii) AP = 5 cm, PB = 6 cm and CD = 13 cm, find CP.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 30.
(a) In the figure (i) given below, PT is a tangent to the circle. Find TP if AT = 16 cm and AB = 12 cm.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
(b) In the figure given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find (i) AB. (ii) the length of tangent PT.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 31.
PAB is secant and PT is tangent to a circle
(i) PT = 8 cm and PA = 5 cm, find the length of AB.
(ii) PA = 4.5 cm and AB = 13.5 cm, find the length of PT.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 32.
In the adjoining figure, CBA is secant and CD is tangent to the circle. If AB = 7 cm and BC = 9 cm, then
(i) Prove that ∆ACD ~ ∆DCB.
(ii) Find the length of CD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 33.
(a) In the figure (i) given below, PAB is secant and PT is tangent to a circle. If PA : AB = 1 : 3 and PT = 6 cm, find the length of PB.
(b) In the figure (ii) given below, ABC is an isosceles triangle in which AB = AC and Q is mid-point of AC. If APB is a secant, and AC is tangent to the circle at Q, prove that AB = 4 AP.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 34.
Two chords AB, CD of a circle intersect externally at a point P. If PA = PC, Prove that AB = CD.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 35.
(a) In the figure (i) given below, AT is tangent to a circle at A. If ∠BAT = 45° and ∠BAC = 65°, find ∠ABC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
(b) In the figure (ii) given below, A, B and C are three points on a circle. The tangent at C meets BA produced at T. Given that ∠ATC = 36° and ∠ACT = 48°, calculate the angle subtended by AB at the centre of the circle. (2001)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 36.
In the adjoining figure, ∆ABC is isosceles with AB = AC. Prove that the tangent at A to the circumcircle of ∆ABC is parallel to BC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 37.
If the sides of a rectangle touch a circle, prove that the rectangle is a square.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 38.
(a) In the figure (i) given below, two circles intersect at A, B. From a point P on one of these circles, two line segments PAC and PBD are drawn, intersecting the other circle at C and D respectively. Prove that CD is parallel to the tangent at P.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
(b) In the figure (ii) given below, two circles with centres C, C’ intersect at A, B and the point C lies on the circle with centre C’. PQ is a tangent to the circle with centre C’ at A. Prove that AC bisects ∠PAB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

Question 39.
(a) In the figure (i) given below, AB is a chord of the circle with centre O, BT is tangent to the circle. If ∠OAB = 32°, find the values of x and y.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
(b) In the figure (ii) given below, O and O’ are centres of two circles touching each other externally at the point P. The common tangent at P meets a direct common tangent AB at M. Prove that:
(i) M bisects AB (ii) ∠APB = 90°.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 1.
If O is the centre of the circle, find the value of x in each of the following figures (using the given information):
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

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Question 2.
(a) In the figure (i) given below, O is the centre of the circle. If ∠AOC = 150°, find (i) ∠ABC (ii) ∠ADC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
(b) In the figure (ii) given below, AC is a diameter of the given circle and ∠BCD = 75°. Calculate the size of (i) ∠ABC (ii) ∠EAF.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 3.
(a) In the figure, (i) given below, if ∠DBC = 58° and BD is a diameter of the circle, calculate:
(i) ∠BDC (ii) ∠BEC (iii) ∠BAC
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
(b) In the figure (if) given below, AB is parallel to DC, ∠BCE = 80° and ∠BAC = 25°. Find:
(i) ∠CAD (ii) ∠CBD (iii) ∠ADC (2008)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 4.
(a) In the figure given below, ABCD is a cyclic quadrilateral. If ∠ADC = 80° and ∠ACD = 52°, find the values of ∠ABC and ∠CBD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
(b) In the figure given below, O is the centre of the circle. ∠AOE =150°, ∠DAO = 51°. Calculate the sizes of ∠BEC and ∠EBC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 5.
(a) In the figure (i) given below, ABCD is a parallelogram. A circle passes through A and D and cuts AB at E and DC at F. Given that ∠BEF = 80°, find ∠ABC.
(b) In the figure (ii) given below, ABCD is a cyclic trapezium in which AD is parallel to BC and ∠B = 70°, find:
(i)∠BAD (ii) DBCD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 6.
(a) In the figure given below, O is the centre of the circle. If ∠BAD = 30°, find the values of p, q and r.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
(b) In the figure given below, two circles intersect at points P and Q. If ∠A = 80° and ∠D = 84°, calculate
(i) ∠QBC (ii) ∠BCP
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 7.
(a) In the figure given below, PQ is a diameter. Chord SR is parallel to PQ.Given ∠PQR = 58°, calculate (i) ∠RPQ (ii) ∠STP
(T is a point on the minor arc SP)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
(b) In the figure given below, if ∠ACE = 43° and ∠CAF = 62°, find the values of a, b and c (2007)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 8.
(a) In the figure (i) given below, AB is a diameter of the circle. If ∠ADC = 120°, find ∠CAB.
(b) In the figure (ii) given below, sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E, the sides AD and BC are produced to meet at F. If x : y : z = 3 : 4 : 5, find the values of x, y and z.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 9.
(a) In the figure (i) given below, ABCD is a quadrilateral inscribed in a circle with centre O. CD is produced to E. If ∠ADE = 70° and ∠OBA = 45°, calculate
(i) ∠OCA (ii) ∠BAC
(b) In figure (ii) given below, ABF is a straight line and BE || DC. If ∠DAB = 92° and ∠EBF = 20°, find :
(i) ∠BCD (ii) ∠ADC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 10.
(a) In the figure (ii) given below, PQRS is a cyclic quadrilateral in which PQ = QR and RS is produced to T. If ∠QPR = 52°, calculate ∠PST.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
(b) In the figure (ii) given below, O is the centre of the circle. If ∠OAD = 50°, find the values of x and y.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 11.
(a) In the figure (i) given below, O is the centre of the circle. If ∠COD = 40° and ∠CBE = 100°, then find :
(i) ∠ADC
(ii) ∠DAC
(iii) ∠ODA
(iv) ∠OCA.
(b) In the figure (ii) given below, O is the centre of the circle. If ∠BAD = 75° and BC = CD, find :
(i) ∠BOD
(ii) ∠BCD
(iii) ∠BOC
(iv) ∠OBD (2009)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 12.
In the given figure, O is the centre and AOE is the diameter of the semicircle ABCDE. If AB = BC and ∠AEC = 50°, find :
(i) ∠CBE
(ii) ∠CDE
(iii) ∠AOB.
Prove that OB is parallel to EC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 13.
(a) In the figure (i) given below, ED and BC are two parallel chords of the circle and ABE, ACD are two st. lines. Prove that AED is an isosceles triangle.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
(b) In the figure (ii) given below, SP is the bisector of ∠RPT and PQRS is a cyclic quadrilateral. Prove that SQ = RS.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 14.
In the given figure, ABC is an isosceles triangle in which AB = AC and circle passing through B and C intersect sides AB and AC at points D and E. Prove that DE || BC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 15.
(a) Prove that a cyclic parallelogram is a rectangle.
(b) Prove that a cyclic rhombus is a square.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

Question 16.
In the given figure, chords AB and CD of the circle are produced to meet at O. Prove that triangles ODB and OAC are similar. Given that CD = 2 cm, DO = 6 cm and BO = 3 cm, area of quad. CABD
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Chapter Test

Question 1.
Draw a straight line AB of length 8 cm. Draw the locus of all points which are equidistant from A and B. Prove your statement.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Chapter Test

Question 2.
A point P is allowed to travel in space. State the locus of P so that it always remains at a constant distance from a fixed point C.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Chapter Test

Question 3.
Draw a line segment AB of length 7 cm. Construct the locus of a point P such that area of triangle PAB is 14 cm².
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Chapter Test

Question 4.
Draw a line segment AB of length 12 cm. Mark M, the mid-point of AB. Draw and describe the locus of a point which is
(i) at a distance of 3 cm from AB.
(ii) at a distance of 5 cm from the point M. Mark the points P, Q, R, S which satisfy both the above conditions. What kind of quadrilateral is PQRS? Compute the area of the quadrilateral PQRS.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Chapter Test

Question 5.
AB and CD are two intersecting lines. Find the position of a point which is at a distance of 2 cm from AB and 1.6 cm from CD.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Chapter Test

Question 6.
Two straight lines PQ and PK cross each other at P at an angle of 75°. S is a stone on the road PQ, 800 m from P towards Q. By drawing a figure to scale 1 cm = 100 m, locate the position of a flagstaff X, which is equidistant from P and S, and is also equidistant from the road.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Chapter Test

Question 7.
Construct a rhombus PQRS whose diagonals PR, QS are 8 cm and 6 cm respectively. Find by construction a point X equidistant from PQ, PS and equidistant from R, S. Measure XR.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Chapter Test

Question 8.
Without using set square or protractor, construct the parallelogram ABCD in which AB = 5.1 cm. the diagonal AC = 5.6 cm and the diagonal BD = 7 cm. Locate the point P on DC, which is equidistant from AB and BC.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Chapter Test

Question 9.
By using ruler and compass only, construct a quadrilateral ABCD in which AB = 6.5 cm, AD = 4 cm and ∠DAB = 75°. C is equidistant from the sides AB and AD, also C is equidistant from the points A and B.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 1.
A point moves such that its distance from a fixed line AB is always the same. What is the relation between AB and the path travelled by P?
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 2.
A point P moves so that its perpendicular distance from two given lines AB and CD are equal. State the locus of the point P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 3.
P is a fixed point and a point Q moves such that the distance PQ is constant, what is the locus of the path traced out by the point Q?
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 4.
(i) AB is a fixed line. State the locus of the point P so that ∠APB = 90°.
(ii) A, B are fixed points. State the locus of the point P so that ∠APB = 60°.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 5.
Draw and describe the locus in each of the following cases :
(i) The locus of points at a distance 2.5 cm from a fixed line.
(ii) The locus of vertices of all isosceles triangles having a common base.
(iii) The locus of points inside a circle and equidistant from two fixed points on the circle.
(iv) The locus of centres of all circles passing through two fixed points.
(v) The locus of a point in rhombus ABCD which is equidistant from AB and AD. (1998)
(vi) The locus of a point in the rhombus ABCD which is equidistant from points A and C.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 6.
Describe completely the locus of points in each of the following cases :
(i) mid-point of radii of a circle.
(ii) centre of a ball, rolling along a straight line on a level floor.
(iii) the point in a plane equidistant from a given line.
(iv) the point in a plane, at a constant distance of 5 cm from a fixed point (in the plane).
(v) centre of a circle of varying radius and touching two arms of ∠ADC.
(vi) centre of a circle of varying radius and touching a fixed circle, centre O, at a fixed point A on it.
(vii) centre of a circle of radius 2 cm and touching a fixed circle of radius 3 cm with centre 0.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 7.
Using a ruler and compasses construct:
(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.
(ii) the locus of points equidistant from A and C.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 8.
Construct triangle ABC, with AB = 7 cm, BC = 8 cm and ∠ABC = 60°. Locate by construction the point P such that:
(i) P is equidistant from B and C and
(ii) P is equidistant from AB and BC
(iii) Measure and record the length of PB. (2000)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 9.
A straight line AB is 8 cm long. Locate by construction the locus of a point which is:
(i) Equidistant from A and B.
(ii) Always 4 cm from the line AB.
(iii) Mark two points X and Y, which are 4 cm from AB and equidistant from A and B. Name the figure AXBY.(2008)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 10.
Use ruler and compasses only for this question.
(i) Construct ∆ABC, where AB = 3.5 cm, BC = 6 cm and ∠ABC = 60°.
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure arid record the length of PB. (2010)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 11.
Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105°. Hence:
(i) Construct the locus of points equidistant from BA and BC.
(ii) Construct the locus of points equidistant from B and C.
(iii) Mark the point which satisfies the above two loci as P. Measure and write the length of PC.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 12.
In the given diagram, A, B and C are fixed collinear points; D is a fixed point outside the line: Locate
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14
(i) the point P on AB such that CP = DP.
(ii) the points Q such that CQ = DQ = 3 cm. How many such points are possible?
(iii) the points R on AB such that DR = 4 cm. How many such points are possible?
(iv) the points S such that CS = DS and S is 4 cm away from the line CD. How many such points are possible?
(v) Are the points P, Q, R collinear?
(vi) Are the points P, Q, S collinear?
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 13.
Points A, B and C represent the position of three towers such that AB = 60 m, BC = 73 m and CA = 52 m. Taking a scale of 10 m to 1 cm, make an accurate drawing of ∆ABC. Find by drawing, the location of a point which is equidistant from A, B and C, and its actual distance from any of the towers.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 14.
Draw two intersecting lines to include an angle of 30°. Use ruler and compasses to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such points exist? (1990)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 15.
Without using set square or protractor, construct the quadrilateral ABCD in which ∠BAD = 45°, AD = AB = 6 cm, BC = 3.6 cm and CD = 5 cm.
(i) Measure ∠BCD.
(ii) Locate the point P on BD which is equidistant from BC and CD. (1992)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 16.
Without using set square or protractor, construct rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Measure ∠ABC. Find the point R on AD such that RB = RC. Measure the length of AR. (1990)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 17.
Without using set-squares or protractor construct :
(i) Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.
(ii) Draw the locus of a point which moves so that it is always 2.5 cm from B.
(iii) Draw the locus of a point which moves so that it is equidistant from the sides BC and CA.
(iv) Mark the point of intersection of the loci with the letter P and measure PC. (1994)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 18.
By using ruler and compasses only, construct an isosceles triangle ABC in which BC = 5 cm, AB = AC and ∠BAC = 90°. Locate the point P such that :
(i) P is equidistant from the sides BC and AC.
(ii) P is equidistant from the points B and C.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 19.
Using ruler and compasses only, construct a quadrilateral ABCD in which AB = 6 cm, BC = 5 cm, ∠B = 60°, AD = 5 cm and D is equidistant from AB and BC. Measure CD. (1983)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 20.
Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB (2001)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 21.
Use ruler and compasses only for this question. Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of length 6 cm and 5 cm respectively.
(i) Construct the locus of points, inside the circle, that is equidistant from A and C. Prove your construction.
(ii) Construct the locus of points, inside the circle, that is equidistant from AB and AC, (1995)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

Question 22.
Ruler and compasses only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct a triangle ABC, in which BC = 6 cm, AB = 9 cm. and ∠ABC = 60°.
(ii) Construct the locus of all points, inside ∆ABC, which are equidistant from B and C.
(iii) Construct the locus of the vertices of the triangles with BC as a base, which is equal in area to ∆ABC.
(iv) Mark the point Q, in your construction, which would make ∆QBC equal in area to ∆ABC, and isosceles.
(v) Measure and record the length of CQ. (1998)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Locus Ex 14

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 1.
In the given figure, ∠1 = ∠2 and ∠3 = ∠4. Show that PT × QR = PR × ST.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 2.
In the adjoining figure, AB = AC. If PM ⊥ AB and PN ⊥ AC, show that PM × PC = PN × PB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 3.
(a) In the figure (1) given below. ∠AED = ∠ABC. Find the values of x and y.
(b) In the fig. (2) given below, CD = \(\\ \frac { 1 }{ 2 } \) AC, B is mid-point of AC and E is mid-point of DF. If BF || AG, prove that:
(i) CE || AG
(ii) 3ED = GD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 4.
In the given figure, 2AD = BD, E is mid-point of BD and F is mid-point of AC and EC || BH. Prove that:
(i) DF || BH
(ii) AH = 3AF.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 5.
In a ∆ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm, find BD and CE.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 6.
In a ∆ABC, D and E are points on the sides AB and AC respectively such that AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and AC = 8.8cm. Is DE || BC? Justify your answer.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 7.
In a ∆ABC, DE is parallel to the base BC, with D on AB and E on AC. If \(\frac { AD }{ DB } =\frac { 2 }{ 3 } ,\frac { BC }{ DE } \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 8.
If the area of two similar triangles are 360 cm² and 250 cm² and if one side of the first triangle is 8 cm, find the length of the corresponding side of the second triangle.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 9.
In the adjoining figure, D is a point on BC such that ∠ABD = ∠CAD. If AB = 5 cm, AC = 3 cm and AD = 4 cm, find
(i) BC
(ii) DC
(iii) area of ∆ACD : area of ∆BCA.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 10.
In the adjoining figure, the diagonals of a parallelogram intersect at O. OE is drawn parallel to CB to meet AB at E, find the area of DAOE : area of ||gm ABCD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 11.
In the given figure, ABCD is a trapezium in which AB || DC. If 2AB = 3DC, find the ratio of the areas of ∆AOB and ∆COD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 12.
In the adjoining figure, ABCD is a parallelogram. E is mid-point of BC. DE meets the diagonal AC at O and meets AB (produced) at F. Prove that
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
(i) DO : OE = 2 : 1
(ii) area of ∆OEC : area of ∆OAD = 1 : 4.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 13.
A model of a ship is made to a scale of 1 : 250. Calculate :
(i) the length of the ship, if the length of the model is 1.6 m.
(ii) the area of the deck of the ship, if the area of the deck of the model is 2.4 m².
(iii) the volume of the model, if the volume of the ship is 1 km³.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Choose the correct answer from the given four options (1 to 22):

Question 1.
In the given figure, ∆ABC ~ ∆QPR. Then ∠R is
(a) 60°
(b) 50°
(c) 70°
(d) 80°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 2.
In the given figure, ∆ABC ~ ∆QPR. The value of x is
(a) 2.25 cm
(b) 4 cm
(c) 4.5 cm
(d) 5.2 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 3.
In the given figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°. Then, ∠PBA is equal to
(a) 50°
(b) 30°
(c) 60°
(d) 100°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 4.
If in two triangles ABC and PQR,
\(\frac { AB }{ QR } =\frac { BC }{ PR } =\frac { CA }{ PQ } \)
then
(a) ∆PQR ~ ∆CAB
(b) ∆PQR ~ ∆ABC
(c) ∆CBA ~ ∆PQR
(d) ∆BCA ~ ∆PQR
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 5.
In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE, then the two triangles are
(a) congruent but not similar
(b) similar but not congruent
(c) neither congruent nor similar
(d) congruent as well as similar
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 6.
In the given figure, if D, E and F are midpoints of the sides BC, CA and AB respectively, then the two triangles ABC and DEF are
(a) similar
(b) congruent
(c) both similar and congruent
(d) neither similar nor congruent
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 7.
The given figure, AB || DE. The length of CD is
(a) 2.5 cm
(b) 2.7 cm
(c) \(\\ \frac { 10 }{ 3 } \) cm
(d) 3.5 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 8.
If in triangles ABC and DEF,\(\frac { AB }{ DE } =\frac { BC }{ FD } \) , then they will be similar when
(a) ∠B = ∠E
(b) ∠A = ∠D
(c) ∠B = ∠D
(d) ∠A = ∠F
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 9.
If ∆PQR ~ ∆ABC, PQ = 6 cm, AB = 8 cm and perimeter of ∆ABC is 36 cm, then perimeter of ∆PQR is
(a) 20.25 cm
(b) 27 cm
(c) 48 cm
(d) 64 cm
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 10.
In the given figure, DE || BC and all measurements are in centimetres. The length of AE is
(a) 2 cm
(b) 2.25 cm
(c) 3.5 cm
(d) 4 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 11.
In the given figure, PQ || CA and all lengths are given in centimetres. The length of BC is
(a) 6.4 cm
(b) 7.5 cm
(c) 8 cm
(d) 9 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 12.
In the given figure, MN || QR. If PN = 3.6 cm, NR = 2.4 cm and PQ = 5 cm, then PM is
(a) 4 cm
(b) 3.6 cm
(c) 2 cm
(d) 3 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 13.
D and E are respectively the points on the sides AB and AC of a ∆ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then the length of DE is
(a) 2.5 cm
(b) 3 cm
(c) 5 cm
(d) 6 cm
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 14.
It is given that ∆ABC ~ ∆PQR with \(\frac { BC }{ QR } =\frac { 1 }{ 3 } \) then \(\frac { area\quad of\quad \Delta PQR }{ area\quad of\quad \Delta ABC } \) equal to
(a) 9
(b) 3
(c) \(\\ \frac { 1 }{ 3 } \)
(d) \(\\ \frac { 1 }{ 9 } \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 15.
If the areas of two similar triangles are in the ratio 4 : 9, then their corresponding sides are in the ratio
(a) 9 : 4
(b) 3 : 2
(c) 2 : 3
(d) 16 : 81
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 16.
If ∆ABC ~ ∆PQR, BC = 8 cm and QR = 6 cm, then the ratio of the areas of ∆ABC and ∆PQR is
(a) 8 : 6
(b) 3 : 4
(c) 9 : 16
(d) 16 : 9
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 17.
If ∆ABC ~ ∆QRP \(\frac { area\quad of\quad \Delta ABC }{ area\quad of\quad \Delta PQR } \) AB = 18 cm and BC = 15 cm, then the length of PR is equal to
(a) 10 cm
(b) 12 cm
(c) \(\\ \frac { 20 }{ 3 } \)
(d) 8 cm
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 18.
If ∆ABC ~ ∆PQR, area of ∆ABC = 81 cm², area of ∆PQR = 144 cm² and QR = 6 cm, then length of BC is
(a) 4 cm
(b) 4.5 cm
(c) 9 cm
(d) 12 cm
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 19.
In the given figure, DE || CA and D is a point on BD such that BD : DC = 2 : 1. The ratio of area of ∆ABC to area of ∆BDE is
(a) 4 : 1
(b) 9 : 1
(c) 9 : 4
(d) 3 : 2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 20.
If ABC and BDE are two equilateral triangles such that D is mid-point of BC, then the ratio of the areas of triangles ABC and BDE is
(a) 2 : 1
(b) 1 : 2
(c) 1 : 4
(d) 4 : 1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 21.
The areas of two similar triangles are 81 cm² and 49 cm² respectively. If an altitude of the smaller triangle is 3.5 cm, then the corresponding altitude of the bigger triangle is
(a) 9 cm
(b) 7 cm
(c) 6 cm
(d) 4.5 cm
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

Question 22.
Given ∆ABC ~ ∆PQR, area of ∆ABC = 54 cm² and area of ∆PQR = 24 cm². If AD and PM are medians of ∆’s ABC and PQR respectively, and length of PM is 10 cm, then length of AD is
(a) \(\\ \frac { 49 }{ 3 } \) cm
(b) \(\\ \frac { 20 }{ 3 } \) cm
(c) 15 cm
(d) 22.5 cm
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 1.
Given that ∆s ABC and PQR are similar.
Find:
(i) The ratio of the area of ∆ABC to the area of ∆PQR if their corresponding sides are in the ratio 1 : 3.
(ii) the ratio of their corresponding sides if area of ∆ABC : area of ∆PQR = 25 : 36.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 2.
∆ABC ~ DEF. If area of ∆ABC = 9 sq. cm., area of ∆DEF =16 sq. cm and BC = 2.1 cm., find the length of EF.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 3.
∆ABC ~ ∆DEF. If BC = 3 cm, EF = 4 cm and area of ∆ABC = 54 sq. cm. Determine the area of ∆DEF.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 4.
The area of two similar triangles is 36 cm² and 25 cm². If an altitude of the first triangle is 2.4 cm, find the corresponding altitude of the other triangle.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 5.
(a) In the figure, (i) given below, PB and QA are perpendiculars to the line segment AB. If PO = 6 cm, QO = 9 cm and the area of ∆POB = 120 cm², find the area of ∆QOA. (2006)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
(b) In the figure (ii) given below, AB || DC. AO = 10 cm, OC = 5cm, AB = 6.5 cm and OD = 2.8 cm.
(i) Prove that ∆OAB ~ ∆OCD.
(ii) Find CD and OB.
(iii) Find the ratio of areas of ∆OAB and ∆OCD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 6.
(a) In the figure (i) given below, DE || BC. If DE = 6 cm, BC = 9 cm and area of ∆ADE = 28 sq. cm, find the area of ∆ABC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
(b) In the figure (iii) given below, DE || BC and AD : DB = 1 : 2, find the ratio of the areas of ∆ADE and trapezium DBCE.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 7.
In the given figure, DE || BC.
(i) Prove that ∆ADE and ∆ABC are similar.
(ii) Given that AD = \(\\ \frac { 1 }{ 2 } \) BD, calculate DE if BC = 4.5 cm.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
(iii) If area of ∆ABC = 18 cm², find the area of trapezium DBCE
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 8.
In the given figure, AB and DE are perpendicular to BC.
(i) Prove that ∆ABC ~ ∆DEC
(ii) If AB = 6 cm: DE = 4 cm and AC = 15 cm, calculate CD.
(iii) Find the ratio of the area of ∆ABC : area of ∆DEC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 9.
In the adjoining figure, ABC is a triangle.
DE is parallel to BC and \(\frac { AD }{ DB } =\frac { 3 }{ 2 } \)
(i) Determine the ratios \(\frac { AD }{ AB }, \frac { DE }{ BC } \)
(ii) Prove that ∆DEF is similar to ∆CBF.
Hence, find \(\\ \frac { EF }{ FB } \).
(iii) What is the ratio of the areas of ∆DEF and ∆CBF ? (2007)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 10.
In ∆ABC, AP : PB = 2 : 3. PO is parallel to BC and is extended to Q so that CQ is parallel to BA. Find:
(i) area ∆APO : area ∆ABC.
(ii) area ∆APO : area ∆CQO. (2008)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 11.
(a) In the figure (i) given below, ABCD is a trapezium in which AB || DC and AB = 2 CD. Determine the ratio of the areas of ∆AOB and ∆COD.
(b) In the figure (ii) given below, ABCD is a parallelogram. AM ⊥ DC and AN ⊥ CB. If AM = 6 cm, AN = 10 cm and the area of parallelogram ABCD is 45 cm², find
(i) AB
(ii) BC
(iii) area of ∆ADM : area of ∆ANB.
(c) In the figure (iii) given below, ABCD is a parallelogram. E is a point on AB, CE intersects the diagonal BD at O and EF || BC. If AE : EB = 2 : 3, find
(i) EF : AD
(ii) area of ∆BEF : area of ∆ABD
(iii) area of ∆ABD : area of trap. AFED
(iv) area of ∆FEO : area of ∆OBC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 12.
In the adjoining figure, ABCD is a parallelogram. P is a point on BC such that BP : PC = 1 : 2 and DP produced meets AB produced at Q. If area of ∆CPQ = 20 cm², find
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
(i) area of ∆BPQ.
(ii) area ∆CDP.
(iii) area of || gm ABCD.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 13.
(a) In the figure (i) given below, DE || BC and the ratio of the areas of ∆ADE and trapezium DBCE is 4 : 5. Find the ratio of DE : BC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
(b) In the figure (ii) given below, AB || DC and AB = 2 DC. If AD = 3 cm, BC = 4 cm and AD, BC produced meet at E, find (i) ED (ii) BE (iii) area of ∆EDC : area of trapezium ABCD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 14.
(a) In the figure given below, ABCD is a trapezium in which DC is parallel to AB. If AB = 9 cm, DC = 6 cm and BB = 12 cm., find
(i) BP
(ii) the ratio of areas of ∆APB and ∆DPC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
(b) In the figure given below, ∠ABC = ∠DAC and AB = 8 cm, AC = 4 cm, AD = 5 cm.
(i) Prove that ∆ACD is similar to ∆BCA
(ii) Find BC and CD
(iii) Find the area of ∆ACD : area of ∆ABC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 15.
ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that:
(i) ∆ADE ~ ∆ACB.
(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
(iii) Find, area of ∆ADE : area of quadrilateral BCED.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 16.
Two isosceles triangles have equal vertical angles and their areas are in the ratio 7 : 16. Find the ratio of their corresponding height.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 17.
On a map is drawn to a scale of 1 : 250000, a triangular plot of land has the following measurements :
AB = 3 cm, BC = 4 cm and ∠ABC = 90°. Calculate
(i) the actual length of AB in km.
(ii) the area of the plot in sq. km:
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 18.
On a map is drawn to a scale of 1 : 25000, a rectangular plot of land, ABCD has the following measurements AB = 12 cm and BG = 16 cm.
Calculate:
(i) the distance of a diagonal of the plot in km.
(ii) the area of the plot in sq. km.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 19.
The model of a building is constructed with scale factor 1 : 30.
(i) If the height of the model is 80 cm, find the actual height of the building in metres.
(ii) If the actual volume of a tank at the top of the building is 27 m³, find the volume of the tank on the top of the model. (2009)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

Question 20.
A model of a ship is made to a scale of 1 : 200.
(i) If the length of the model is 4 m, find the length of the ship.
(ii) If the area of the deck of the ship is 160000 m², find the area of the deck of the model.
(iii) If the volume of the model is 200 litres, find the volume of the ship in m³. (100 litres = m³)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.3

ML Aggarwal Class 10 Solutions for ICSE Maths