## 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°

Solution:

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°

Solution:

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°

Solution:

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°

Solution:

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:

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°

Solution:

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°

Solution:

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°

Solution:

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°

Solution:

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:

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:

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:

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°

Solution:

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:

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

Solution:

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:

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:

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°

Solution:

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°

Solution:

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°

Solution:

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

Solution:

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

Solution:

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:

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°

Solution:

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°

Solution:

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

Solution:

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

Solution:

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°

Solution:

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

Solution: