Please refer to the MCQ Questions for Class 9 Mathematics Chapter 10 Circles with Answers. The following Circles Class 9 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 9. Our experts have designed MCQ Questions for Class 9 Mathematics with Answers for all chapters in your NCERT Class 9 Mathematics book.

## Circles Class 9 MCQ Questions with Answers

See below Circles Class 9 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question. 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) 30°

(b) 50°

(c) 40°

(d) 60°

## Answer

B

**Question. Angle formed in minor segment of a circle is**

(a) an acute angle

(b) an obtuse angle

(c) a right angle

(d) a straight angle

## Answer

B

**Question. Number of circles that can be drawn through three non-collinear points is**

(a) 1

(b) 0

(c) 2

(d) 3

## Answer

A

**Question. In the given figure, ABCD is a cyclic quadrilateral,∠CBQ = 48° and a = 2b. Then, b is equal to**

(a) 48°

(b) 38°

(c) 28°

(d) 18°

## Answer

C

**Question. The figure shows two circles which intersect at A and B. The centre of the smaller circle is O and it lies on the circumference of the larger circle. If ∠APB = 70°, then the measure of ∠ACB is**

(a) 50°

(b) 60°

(c) 70°

(d) 40°

## Answer

D

**Question. In the given figure, O is the centre of the circle. ∠BAO = 68°. AC is a diameter of the circle. The measure of ∠BCO is**

(a) 22°

(b) 33°

(c) 44°

(d) 68°

## Answer

A

**Question. P is a point on the diameter AB of a circle and CD is a chord perpendicular to AB. If AP = 4 cm and PB = 16 cm then the length of chord CD is**

(a) 20 cm

(b) 10 cm

(c) 8 cm

(d) 16 cm

## Answer

D

**Question. Chords AB and CD intersect at right angles. If ∠BAC = 40°, then ∠ABD is equal to**

(a) 45°

(b) 60°

(c) 50°

(d) 40°

## Answer

C

**Question. If ABCD is a cyclic trapezium in which AD ∥ BC and ∠B = 60°, then ∠BCD is equal to**

(a) 120°

(b) 100°

(c) 80°

(d) 60°

## Answer

D

**Question. In the given figure, if ∠CAB = 49° and ∠ADC = 43°, then the measure of ∠ACB is**

(a) 96°

(b) 74°

(c) 92°

(d) 88°

## Answer

D

**Question. In the given figure, if ∠CDB = 40°, then the measure of ∠PAC is**

(a) 160°

(b) 120°

(c) 100°

(d) 140°

## Answer

D

**Question. If a straight line APQB is drawn to cut two concentric circles, then**

(a) AP > BQ

(b) AP = BQ

(c) AP < BQ

(d) AQ > PB

## Answer

B

**Question. In the given figure, if ∠CAB = 50° and ∠CBA = 70°, then ∠ADB is equal to**

(a) 80°

(b) 60°

(c) 50°

(d) 70°

## Answer

B

**Question. If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is**

(a) 8 cm

(b) 6 cm

(c) 12 cm

(d) 10 cm

## Answer

D

**Question. In the given figure, if ∠ADC = 118°, then the measure of ∠BDC is**

(a) 22°

(b) 28°

(c) 32°

(d) 38°

## Answer

B

**Question. ABCD is a parallelogram. A circle passes through A and D and cuts AB at E and DC at F. If ∠BEF = 80°, then ∠ABC is equal to**

(a) 75°

(b) 120°

(c) 100°

(d) 80°

## Answer

D

**Question. If a chord of a circle is equal to its radius, then the angle subtended by this chord in major segment is**

(a) 90°

(b) 60°

(c) 45°

(d) 30°

## Answer

D

**Question. In the given figure, PQ and RS are two equal chords of a circle with centre O. OA and OB are perpendiculars on chords PQ and RS, respectively. If ∠AOB = 140°, then ∠PAB is equal to**

(a) 50°

(b) 70°

(c) 60°

(d) 40°

## Answer

B

**Question. In the given figure, if ∠ABC = 50° and ∠BDC = 40°, then ∠BCA is equal to**

(a) 100°

(b) 40°

(c) 90°

(d) 50°

## Answer

C

**Question. The value of x in the given figure is**

(a) 35°

(b) 45°

(c) 25°

(d) 30°

## Answer

A

**Question. In the given figure, AC is a diameter of the given circle and ∠BCD = 75°. Then, ∠EAF – ∠ABC is equal to**

(a) 10°

(b) 15°

(c) 20°

(d) 25°

## Answer

B

**Question. Greatest chord of a circle is called its**

(a) radius

(b) diameter

(c) chord

(d) secant

## Answer

B

**Question. In the given figure, O is the centre of the circle. ∠OAB and ∠OCB are 40° and 30° respectively. Then, the measure of ∠AOC is**

(a) 120°

(b) 140°

(c) 170°

(d) 110°

## Answer

B

**Question. If ∠OAB = 40°, then the measure of ∠ACB is**

(a) 40°

(b) 80°

(c) 50°

(d) 20°

## Answer

C

**Question. BC is a diameter of the circle and ∠BAO = 60°. Then ∠ADC is equal to**

(a) 60°

(b) 45°

(c) 30°

(d) 90°

## Answer

A

**Question. In the given figure, if ∠BAC = 25°, then ∠BOC is equal to**

(a) 25°

(b) 50°

(c) 60°

(d) 125°

## Answer

B

**Question. In the given figure, O is the centre of the circle and ∠CBE = 25° and ∠DEA = 60°. The measure of ∠ADB is**

(a) 90°

(b) 85°

(c) 95°

(d) 120°

## Answer

C

**Question. In the given figure, ∠ABC = 45°, then the measure of ∠AOC is**

(a) 45°

(b) 90°

(c) 60°

(d) 75°

## Answer

B

**Question. In the given figure, ∠BPC = 19°, arc AB = arc BC = arc CD. Then, the measure of ∠APD is**

(a) 38°

(b) 59°

(c) 57°

(d) 76°

## Answer

C

**Question. O is the centre of the given circle. If ∠APB = 120° and ∠DBC = 25°, then the measure of ∠ADB is equal to**

(a) 120°

(b) 60°

(c) 100°

(d) 95°

## Answer

D

**Question. In the given figure, O is the centre of the circle. If ∠DBA = 35°, then the measure of ∠ACB is equal to**

(a) 35°

(b) 45°

(c) 55°

(d) 65°

## Answer

C

**Question. The given figure shows two intersecting circles. If ∠ABC = 75°, then the measure of ∠PAD is**

(a) 125°

(b) 150°

(c) 75°

(d) 105°

## Answer

D

**Question. In the given figure, AD is the diameter of the circle and AE = DE. If ∠ABC = 115°, then the measure of ∠CAE is**

(a) 60°

(b) 80°

(c) 70°

(d) 90°

## Answer

C

**Question. In the given figure, O is the centre of the circle. ABE is a straight line. If ∠DBE = 95°, then ∠AOD is equal to**

(a) 170°

(b) 190°

(c) 180°

(d) 175°

## Answer

A

**Question. In the given figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to**

(a) 2 cm

(b) 3 cm

(c) 4 cm

(d) 5 cm

## Answer

A

**Question. AOB is the diameter of the circle. If ∠AOE = 150°, then the measure of ∠CBE is**

(a) 105°

(b) 120°

(c) 125°

(d) 115°

## Answer

A

**Question. The region between a chord and either of the arc is called**

(a) a segment

(b) a semicircle

(c) a quarter circle

(d) a sector

## Answer

A

**Question. In the given figure, AB is a side of a regular five sided polygon and AC is a side of a regular six sided polygon inscribed in the circle with centre O. AO and CB intersect at P, then ∠APB is equal to**

(a) 100°

(b) 72°

(c) 96°

(d) 90°

## Answer

C

**Question. AOB is a diameter of the circle and C, D, E are any three points on the semicircle. Then, ∠AED + ∠BCD is equal to**

(a) 25°

(b) 260°

(c) 270°

(d) 280°

## Answer

C

**Question. What fraction of the whole circle is minor arc RP in the given figure?**

(a) 12 of the circle

(b) 14 of the circle

(c) 13 of the circle

(d) 15 of the circle

## Answer

C

**Question. In the given circle, O is the centre and ∠BDC = 42°.Then, ∠ACB is equal to**

(a) 42°

(b) 48°

(c) 58°

(d) 52°

## Answer

B

**Question. In the given figure, AB ∥ CD and O is the centre of the circle. If ∠ADC = 25°, then the measure of ∠AEB is**

(a) 80°

(b) 50°

(c) 25°

(d) 40°

## Answer

D

**Question. In the given figure, ∠OPQ = 30° and ∠ORQ = 57°.Then, the measure of ∠POR is**

(a) 33°

(b) 57°

(c) 66°

(d) 54°

## Answer

D

**Question. In the given figure, O is the centre of the circle and ∠SPQ = 50°. Then, the measure of ∠SRQ is**

(a) 100°

(b) 130°

(c) 120°

(d) 110°

## Answer

B

**Question. In the given figure, M, A, B and N are points on a circle having centre O. AN and MB cut at Y. If ∠NYB = 50° and ∠YNB = 20°, then reflex ∠MON is equal to**

(a) 200°

(b) 220°

(c) 240°

(d) 260°

## Answer

B

**Question. In the given figure, ABCD is a quadrilateral inscribed in a circle with centre O. CD is produced to E. If ∠ADE = 95° and ∠OBA = 30°, then ∠OAC is equal to**

(a) 10°

(b) 5°

(c) 15°

(d) 20°

## Answer

B

**Question. In the given figure, ABCD is a cyclic quadrilateral in which ∠BAD = 75°, ∠ABD = 58° and ∠ADC = 77°, AC and BD intersect at P. Then, the measure of ∠DPC is**

(a) 94°

(b) 90°

(c) 92°

(d) 105°

## Answer

C

**Question. AD is a diameter of a circle and AB is a chord. If AD = 50 cm, AB = 48 cm, then the distance of AB from the centre of the circle is**

(a) 5 cm

(b) 6 cm

(c) 7 cm

(d) 8 cm

## Answer

C

**Question. In the given figure, if ∠AOB = 80° and ∠ABC = 30°, then ∠CAO is equal to**

(a) 30°

(b) 80°

(c) 60°

(d) 40°

## Answer

C

**Question. In the given figure, chords AB and CD intersect at P. If ∠DPB = 88° and ∠DAP = 46°, then the measure of ∠ABC is**

(a) 48°

(b) 42°

(c) 46°

(d) 44°

## Answer

B

**Question. In the given figure, AB is a diameter of the circle APBR. APQ and RBQ are straight lines. If ∠A = 35° and ∠Q = 25°, then the measure of ∠PBR is**

(a) 135°

(b) 115°

(c) 155°

(d) 165°

## Answer

B

**Question. The given figures show two congruent circles with centre O and O′. Arc AXB subtends an angle of 75° at the centre and arc A′YB′ subtends an angle of 25° at the centre O′. Then, the ratio of arcs AXB to A′YB′ is**(a) 3 : 1

(b) 1 : 3

(c) 2 : 1

(d) 1 : 2

## Answer

A

**Question. In the given figure, P and Q are centres of two circles intersecting at B and C. ACD is a straight line. Then, the measure of ∠BQD is**

(a) 115°

(b) 150°

(c) 105°

(d) 130°

## Answer

B

**Question. The given figure shows two congruent circles with centre O and O′ intersecting at A and B. If ∠AO′B = 50°, then the measure of ∠APB is**

(a) 50°

(b) 40°

(c) 25°

(d) 45°

## Answer

C

**Question. AB is a chord of a circle with radius ‘r’. If P is any point on the circle such that ∠APB is a right angle, then AB is equal to**

(a) r

(b) 2r

(c) 3r

(d) r2

## Answer

B