Please refer to the **MCQ Questions for Class 10 Maths Circles **with Answers. The following Circles Class 10 Maths MCQ Questions have been designed based on the current academic year syllabus and examination guidelines for Class 10. Our faculty has designed MCQ Questions for Class 10 Maths with Answers for all chapters as per your NCERT Class 10 Mathematics book.

## Circles Class 10 MCQ Questions with Answers

Please see below Circles Class 10 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question. AB is a diameter of a circle with centre O. Tangent ST touches the circle at C. If ∠ BAC = 40° , find ∠ACT .**

(a) 50°

(b) 30°

(c) 60°

(d) 40°

## Ans.

A

**Question.** In the given figure, AB is a tangent at P.

**Find ∠APD.**

(a) ∠PDE

(b) ∠EPB

(c) ∠DPE

(d) ∠PED

## Ans.

D

**Question.** Two circles of radii 8 cm and 2 cm have direct common tangent of length 10 cm, find the distance between their centres.

(a) 8cm

(b) 10cm

(c) 21 cm

(d) 200 cm

## Ans.

A

**Question.** Two circles with centres 0 and P, and radii 8 cm and 4 cm touch each other externally. Find the length of their common tangent QR.

(a) 8cm

(b) 7cm

(c) 8√2cm

(d) 7√3cm

## Ans.

C

**Question.** If the four sides of a quadrilateral ABCD are tangential to a circle, which of the following is true?

(a) AC + AD = BD + CD

(b) AB + CD = BC +AD

(c) AB + CD = AC + BD

(d) AC + AD = BC + AB

## Ans.

B

**Question.** In the figure, find ∠ABC

(a) 60^{0}

(b) 120^{0}

(c) 180^{0 }

(d) 90^{0}

## Ans.

A

**Question.** A tangent ST, touches a circle at B.AB is a chord such that ∠ABT = 65°

Find ∠AOB , where O is the centre of the circle.

(a) 120°

(b) 145°

(c) 110°

(d) 130°

## Ans.

D

**Question.****In the given figure, a circle touches the side BC of ΔABC at P and touches AB and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter of ΔABC**

(a) 6cm

(b) 10cm

(c) 12cm

(d) 15cm

## Ans.

B

**Question.** A If all the sides of a parallelogram touch a circle, what is the parallelogram?

(a) A rectangle

(b) A rhombus

(c) A square

(d) A trapezium**(22-25): OA and OB are radii and PA and PB are tangents of the circle, as shown in the given figure. **

## Ans.

A

**Question. A tangent CQ touches a circle with centre O at P. Diameter AB is produced to meet the tangent at C. If ∠ACP = a° and ∠BPC = b° , find the relation connecting a and b.**

(a) a° + b° = 180°

(b) a° + 2b° = 90°

(c) a° – b° = 60°

(d) 2a° – b° = 100°

## Ans.

B

**Question.** In the given figure, OA and OB are two radii of the circle. If PA and PB are tangents to the circle at A and B respectively which is the correct statement?6. If the four sides of a quadrilateral ABCD are tangential to a circle, which of the following is true?

(a) AC + AD = BD + CD

(b) AB + CD = BC +AD

(c) AB + CD = AC + BD

(d) AC + AD = BC + AB

(a)∠**AOB** and ∠**APB **are the supplementary angles.

(b) ∠**PBO** and ∠**APB** are complementary angles.

(c) ∠**PBO **and ∠**AOB** are complementary angles.

(d) Both (a) and (c)

## Ans.

A

**Question.** Three circles with centres A,B and C touch one another externally. The three centres are joined to one another to form a triangle.

If AB = 7 cm, BC = 11 cm and AC = 6 cm, find the radii of the three circles.

(a) 2 cm, 7 cm, 9 cm

(b) 1 cm, 6 cm, 5 cm

(c) 12 cm, 5 cm, 6 cm

(d) 3cm, 10 cm, 7 cm

## Ans.

B

**Question.** If AP= 15 cm and the radius is 8 cm, find the distance of P from the centre of the circle.

(a) 12cm

(b) 15cm

(c) 17cm

(d) 20cm

## Ans.

C

**Question.** In the given figure.TP and TQ are tangents to the circle. If ∠PAQ = 70^{0} , what is ∠PTQ?

(a) 30^{0}

(b) 45^{0}

(c) 60^{0}

(d) 40^{0}

## Ans.

D

**Question.** If the distance between two circles of radii R and r is d, find the length of the direct common tangent.

(a)√d^{2} + (R – r)^{2}

(b)√d^{2} – (R + r)^{2}

(c) √R^{2} +r)2 + d^{2}

(d) √d^{2} – (R – r)^{2}

## Ans.

D

**One Word Question :**

**Question. If ∠LOM = 1050 . What is OLN . **

**Answer**

90^{0}

**Question. Find perimeter of quadrilateral PQRS. **

**Answer**

34cm

**Question. BQ, AP and QP are tangents to circle with centre O. Find ∠QOP ? **

**Answer**

90°

**Question. In the figure, a circle touches all the four sides of a quad. ABCD; then which side of the quad, is equal to (AR+BT)? **

**Answer**

AB

**Question. Find LNM in figure 10. **

**Answer**

75^{0}

**Question. Find the perimeter of the quadrilateral ABCD. **

**Answer**

52cm

**Question. How many tangents are there in this figure? **

**Answer**

1

**Question. In the figure if XY=20cm., find perimeter of ΔXLM **

**Answer**

40cm

**Question. What is the similarity between quadrilateral PZXY and a cyclic quadrilateral? **

**Answer**

sum of opposite angles is 180^{0}

**Question. Find radius of the circle. **

**Answer**

√88

**Question. In fig. a chord AB of the larger of the two concentric circles is tangent to the smaller circle at P. If AP = 4.5cm. Find BQ. **

**Answer**

4.5cm

**Question. In figure, if AQ = 5cm, find the perimeter of ΔABC **

**Answer**

10cm

**Question. Find OP when RS = 24cm. **

**Answer**

5cm

**Question. Find the distance between two parallel tangents to a circle whose radius is 5.5cm. **

**Answer**

11cm.

**Question. Find ∠QOP **

**Answer**

110^{0}

**Question. Find OB when AB = 48cm. **

**Answer**

25cm

**Question. How many lines in this figure are touching the circle? **

**Answer**

0

**Question. Find AB. **

**Answer**

24cm

**Question. Find ∠QOP **

**Answer**

50^{0}

**Question. Find PR in the given figure. **

**Answer**

12cm