# MCQs For NCERT Class 9 Mathematics Chapter 10 Circles

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°

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

B

Question. Number of circles that can be drawn through three non-collinear points is
(a) 1
(b) 0
(c) 2
(d) 3

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°

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°

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°

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

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°

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°

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°

D

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

(a) 160°
(b) 120°
(c) 100°
(d) 140°

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

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°

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

D

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

(a) 22°
(b) 28°
(c) 32°
(d) 38°

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°

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°

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°

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°

C

Question. The value of x in the given figure is

(a) 35°
(b) 45°
(c) 25°
(d) 30°

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°

B

Question. Greatest chord of a circle is called its
(b) diameter
(c) chord
(d) secant

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°

B

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

(a) 40°
(b) 80°
(c) 50°
(d) 20°

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°

A

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

(a) 25°
(b) 50°
(c) 60°
(d) 125°

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°

C

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

(a) 45°
(b) 90°
(c) 60°
(d) 75°

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°

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°

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°

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°

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°

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°

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

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°

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

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°

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°

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

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°

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°

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°

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°

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°

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°

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°

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

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°

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°

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°

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

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°

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°