# MCQ Questions for Class 10 Circles

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) 600
(b) 1200
(c) 1800
(d) 900

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 = 700 , what is ∠PTQ?

(a) 300
(b) 450
(c) 600
(d) 400

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)√d2 + (R – r)2
(b)√d2 – (R + r)2
(c) √R2 +r)2 + d2
(d) √d2 – (R – r)2

Ans.

D

One Word Question :

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

900

Question. Find perimeter of quadrilateral PQRS.

34cm

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

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)?

AB

Question. Find LNM in figure 10.

750

Question. Find the perimeter of the quadrilateral ABCD.

52cm

Question. How many tangents are there in this figure?

1

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

40cm

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

sum of opposite angles is 1800

Question. Find radius of the circle.

√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.

4.5cm

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

10cm

Question. Find OP when RS = 24cm.

5cm

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

11cm.

Question. Find ∠QOP

1100

Question. Find OB when AB = 48cm.

25cm

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

0

Question. Find AB.

24cm

Question. Find ∠QOP