# MCQ Chapter 10 Circles Class 10 Mathematics

Please refer to Circles MCQ Questions Class 10 Mathematics below. These MCQ questions for Class 10 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Circles will help you to prepare for the exams and get more marks.

## Circles MCQ Questions Class 10 Mathematics

Please see solved MCQ Questions for Circles in Class 10 Mathematics. All questions and answers have been prepared by expert faculty of standard 10 based on the latest examination guidelines.

### MCQ Questions Class 10 Mathematics Circles

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

B

Question. ABC is a right – angled triangle with ∠B= 90° , AB=12cm and AC=13cm.A circle with centre 0 is inscribed inside the triangle.

Find the radius of the circle.
(a) 8cm
(b) 7cm
(c) 4 cm
(d) 2 cm

D

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?

(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)

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

B

Question. If OA and OB are radii and PA and PB are tangents to the circle, which of the following is quadrilateral OAPB?
(a) Rectangle
(b) Square
(c) Parallelogram
(d) Kite

D

Question. A tangent ST at P to a circle at P is parallel to a chord QR of the circle.

Which of the following is correct statement?
(a) P is equidistant from the extremities of the chord.
(b) PT is the tangent parallel to the chord PQ.
(c) PT is the tangent parallel to the cord PR.
(d) S is equidistant from the extremities of the chord.

A

Question. Tangents AP and AQ are drawn to a circle with centre 0 from an external point A.

Identify the correct statement.
(a) ∠PAQ= 2∠OPQ
(b) ∠PAQ=∠OPQ
(c) ∠PQA =∠QPA
(d) ∠PQA = 2∠OPA

A

Question. In the given figure, OA is a radius and AB is a tangent to the circle. (Note that BC is the shortest distance between B and the circle).lf OA= 12cm and AB = 16 cm, find the distance between B and C.

(a) 7cm
(b) 6cm
(c) 8cm
(d) 12cm

C

Question. A circle with centre 0 and radius 5 cm is inscribed in an equilateral triangle ABC.

Find the perimeter of ΔABC.
(a) 15 √3cm
(b) 25 √2 cm
(c) 14 √2 cm
(d) 30 √3cm

D

Question. An isosceles triangle in which AB = AC is inscribed in a circle.

Which of the following is true?
(a) Tangent at A is parallel to BC.
(b) Tangent at A is perpendicular to AB.
(c) Tangent at A is parallel to AC.
(d) Tangent at A is perpendicular to BC.

A

Question. AP is a secant and PT is a tangent to a circle. Lf PT=15cm and AB = 8BP, find AP.

(a) 45 cm
(b) 36 cm
(c) 25 cm
(d) 62 cm

A

Question. PT is a tangent and PAB is a secant of the circle meeting the circle at A and B. If PA = 4 cm and AB = 5 cm. What is the length of PT?
(a) 8 cm
(b) 6 cm
(c) 3 cm
(d) 1 cm

B

Question. PT and QT are tangents drawn to the circle with centre O. If OT= 25 cm and OP = 15cm, find QT.

(a) 20cm
(b) 10cm
(c) 5cm
(d) 15cm

A

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

B

Question. In the given figure.TP and TQ are tangents to the circle. If ∠PAQ= 70° , what is ∠PTQ?

(a) 30°
(b) 45°
(c) 60°
(d) 40°

D

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°

A

Question. If an equilateral triangle ABC is inscribed in a circle, which of the following is formed by the tangents at their vertices?
(a) A scalene triangle
(b) An equilateral triangle
(c) An isosceles triangle
(d) A right triangle

B

Question. If the four sides of a quadrilateral ABCD are tangential to a circle, which of the following is true?
(c) AB+CD=AC+BD

B

Question. In the given figure, ABCD is a quadrilateral in which ∠Q = 90° . A circle C (O, r) touches the sides AB, BC, CD and DA at P, Q, R, S respectively. If BC = 38 cm, CD = 25 cm, and BP = 27 cm, find the value of r.

(a) 14cm
(b) 15cm
(c) 10cm
(d) 16cm

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

C

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

Find∠APD.
(a) ∠PDE
(b) ∠EPB
(c) ∠DPE
(d) ∠PED

D

Question. In the given figure, two circles with centres A and B of radii 5 cm and 3 cm touch each other internally.

If the perpendicular bisector of segment AB meets the bigger circle in P and Q, find the length of PQ.
(a) 4 √6cm
(b) √24 cm
(c) 8 √3cm
(d) 4 √3cm

B

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°

B

Question. In the figure, find ∠ABC.

(a) 60°
(b) 120°
(c) 180°
(d) 90°

A

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) √(R + r)2 + d2
(d) √d2 – (R – r)2

D

Question. In ΔABC, ∠B= 90° .If a circle drawn with AB as diameter intersects the hypotenuse AC at P, which of the following is true?

(a) The tangent drawn to the circle at P bisects the side BC.
(b) The tangent drawn to the circle at A bisects the side AB.
(c) The tangent drawn to the circle at B bisects the side AC.
(d) The tangent drawn to the circle at C bisects the side BC.

A

Question. BD and CD are two tangents drawn to a circle with centre O.

If∠BDC = 44° ,find ∠BAC.
(a) 68°
(b) 32°
(c) 44°
(d) 96°

A

Question. In the given figure, 0 is the centre of the circle. PQ is the tangent to the circle and secant PAB passes through the centre O.

If PQ =5 cm and PA = 1 cm, find the radius of the circle.
(a) 8cm
(b) 12cm
(c) 10cm
(d) 6cm

B

Question. In the given figure, 0 is the centre of in circle inscribed in ΔABC.

Find ∠BOC if ∠BAC = 40°.
(a) 100°
(b) 120°
(c) 90°
(d) 110°

D

Question. If PB = 20 cm and OA = 15 cm, find the shortest distance between the circle and P.
(a) 25 cm
(b) 15 cm
(c) 30cm
(d) 10cm

D

Question. In the given circle, O is the centre, QP is a diameter and PT is a tangent. If ∠QOS =120° , find ∠PTS.

(a) 30°
(b) 40°
(c) 60°
(d) 80°

C

Question. If ∠APO=18° , find ∠AOB.
(a) 24°
(b) 144°
(c) 108°
(d) 1 75°

B

Question. PQ is a chord of a circle, which on producing, meets the tangent TR at R. If PQ = 5 cm and QR = 4 cm, find TR.

(a) 3 cm
(b) 6 cm
(c) 9cm
(d) 10cm

B

Question. What is the number of common tangents that can be drawn to two intersecting circles touching at two points?
(a) 2
(b) 4
(c) 3
(d) 1

A

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

A

Question. Two concentric circle have their centres at O. OP = 4 cm and OQ = 5 cm. AB is a chord of the circle and a tangent to the inner circle at P.

Find the length of AB.
(a) 6 cm
(b) 5 cm
(c) 8 cm
(d) 9 cm

A

Question. Find ∠APBif ∠OPB= 25° .
(a) 50°
(b) 40°
(c) 70°
(d) 25°

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°

D

Question. With the vertices of a ∠ABC as centres, three circles are described, each touching the other two externally. If the sides of the triangle are 9 cm, 7 cm and 6 cm, find the radii of the circles.

(a) 4 cm, 7 cm and 3 cm
(b) 7 cm, 5 cm and 2 cm
(c) 5 cm, 4 cm and 3 cm
(d) 4 cm, 5 cm and 2 cm

D

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

C

Question. 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° , find the angle subtended by AB at the centre of the circle.

(a) 90°
(b) 96°
(c) 108°
(d) 1 20°

B

Question. PQ is a chord of a circle .the tangent XR at X on the circle cuts PQ produced at R. If XR =12 cm , PQ = x cm, QR = (x – 2)cm , find x in cm.
(a) 6
(b) 7
(c) 10
(d) 14

C

Question. In the given figure, ABC is an isosceles triangle in which AB = AC.A circle through B touches AC at its mid-point D and intersects AB at P.

Which of the following is correct?
(a) AP = 3/4 AB
(b) AP = 2/3 AB
(c) AP = 4/5 AB
(d) AP = 1/4 AB

D

Question. Find the value of x.

(a) 5/2
(b) 8/3
(c) 6/5
(d) 9/4

D

Question. A circle with centre 0 is inscribed in an isosceles triangle PQR in which PQ = PR= 17 cm and QR = 16 cm.

Find the radius of the circle.
(a) 6.2 cm
(b) 4.8 cm
(c) 5.6 cm
(d) 7.4 cm