# MCQ Questions for Class 10 Maths Chapter 10 Circles with Answers

Students are advised to solve the Circles Multiple Choice Questions of Class 10 Maths to know different concepts. Practicing the MCQ Questions on Circles Class 10 with answers will boost your confidence thereby helping you score well in the exam.

Explore numerous MCQ Questions of Circles Class 10 with answers provided with detailed solutions by looking below.

Question 1.

Two circle touch each other externally at C and AB is a common tangent to the circles. Then, ∠ACB =

(a) 60°

(b) 45°

(c) 30°

(d) 90°

## Answer

Answer: (d) 90°

Question 2.

If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal to

(a) 60°

(b) 70°

(c) 80°

(d) 90°

## Answer

Answer: (b) 70°

Question 3.

Tangents from an external point to a circle are

(a) equal

(b) not equal

(c) parallel

(d) perpendicular

## Answer

Answer: (a) equal

Question 4.

Two parallel lines touch the circle at points A and B respectively. If area of the circle is 25 n cm^{2}, then AB is equal to

(a) 5 cm

(b) 8 cm

(c) 10 cm

(d) 25 cm

## Answer

Answer: (c) 10 cm

Question 5.

A line through point of contact and passing through centre of circle is known as

(a) tangent

(b) chord

(c) normal

(d) segment

## Answer

Answer: (c) normal

Question 6.

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q

(a) √119 cm

(b) 13 cm

(c) 12 cm

(d) 8.5 cm

## Answer

Answer: (a) √119 cm

Question 7.

From a point P 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 cm^{2}

(b) 65 cm^{2}

(c) 30 cm^{2}

(d) 32.5 cm^{2}

## Answer

Answer: (a) 60 cm^{2}

Question 8.

At point A on a diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY at a distance 16 cm from A is

(a) 8 cm

(b) 10 cm

(c) 16 cm

(d) 18 cm

## Answer

Answer: (c) 16 cm

Question 9.

The tangents drawn at the extremities of the diameter of a circle are

(a) perpendicular

(b) parallel

(c) equal

(d) none of these

## Answer

Answer: (b) parallel

Question 10.

A circle is inscribed in a ΔABC having AB = 10cm, BC = 12cm and CA = 8cm and touching these sides at D, E, F respectively. The lengths of AD, BE and CF will be

(a) AD = 4cm, BE = 6cm, CF = 8cm

(b) AD = 5cm, BE = 9cm, CF = 4cm

(c) AD = 3cm, BE = 7cm, CF = 5cm

(d) AD = 2cm, BE = 6cm, CF = 7cm

## Answer

Answer:

Question 11.

If four sides of a quadrilateral ABCD are tangential to a circle, then

(a) AC + AD = BD + CD

(b) AB + CD = BC + AD

(c) AB + CD = AC + BC

(d) AC + AD = BC + DB

## Answer

Answer: (b) AB + CD = BC + AD

Question 12.

PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR = 120°, then ∠OPQ is

(a) 60°

(b) 45°

(c) 30°

(d) 90°

## Answer

Answer: (c) 30°

Question 13.

Number of tangents drawn at a point of the , circle is/are

(a) one

(b) two

(c) none

(d) infinite

## Answer

Answer: (a) one

Question 14.

The maximum number of common tangents that can be drawn to two circles intersecting at two distinct point is

(a) 2

(b) 4

(c) 1

(d) 3

## Answer

Answer: (a) 2

Question 15.

In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centre of the circle, then the length of OP is:

(a) 30cm

(b) 31cm

(c) 28cm

(d) 25cm

## Answer

Answer: (d) 25cm

Question 16.

If tangents PA and PB from a 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) 80°

## Answer

Answer: (a) 50°

Question 17.

Segment joining the points of contact of two parallel tangents

(a) may or may not pass through the centre.

(b) will pass through the centre.

(c) will not pass through the centre.

(d) none of these

## Answer

Answer: (b) will pass through the centre.

Question 18.

The length of a tangent drawn from a point at a distance of 10 cm of circle is 8 cm. The radius of the circle is

(a) 4 cm

(b) 5 cm

(c) 6 cm

(d) 7 cm

## Answer

Answer: (c) 6 cm

Question 19.

The length of tangents drawn from an external point to the circle

(a) are equal

(b) are not equal

(c) sometimes are equal

(d) are not defined

## Answer

Answer: (a) are equal

Question 20.

A tangent is drawn from a point at a distance of 17 cm of circle C(0, r) of radius 8 cm. The length of its tangent is

(a) 5 cm

(b) 9 cm

(c) 15 cm

(d) 23 cm

## Answer

Answer: (c) 15 cm

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