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9th Class - Math | Chapter: Circles MCQs

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Q1) The radius of a circle is 13 cm and the length of one of its chords is 10 cm. The distance of the chord from the centre is

(A) 11.5 cm

(B) 12 cm

(D) 23 cm

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Q2) A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. The length of the chord is

(A) 25 cm

(B) 12.5 cm

(D) 9 cm

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Q3) In the given figure, BOC is a diameter of a circle and AB = AC. Then, ∠ABC =

(A) 30°

(B) 45°

(D) 90°

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Q4) In the given figure, O is the centre of a circle. If ∠OAB = 40° and C is a point on the circle, then ∠ACB =

(A) 40°

(B) 50°

(D) 100°

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Q5) AB and CD are two equal chords of a circle with centre O such that ∠AOB = 80°, then ∠COD =

(A) 100°

(B) 80°

(D) 40°

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Q6) The center of the circle lies in______ of the circle.

(A) Interior

(B) Exterior

(D) None of the above

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Q7) The longest chord of the circle is

(A) Radius

(B) Arc

(D) Segment

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Q8) Equal _____ of the congruent circles subtend equal angles at the centers.

(A) Segments

(B) Radii

(D) Chords

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Q9) If chords AB and CD of congruent circles subtend equal angles at their centres, then:

(A) AB = CD

(B) AB > CD

(D) None of the above

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Q10) If there are two separate circles drawn apart from each other, then the maximum number of common points they have

(A) 0

(B) 1

(D) 3

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Q11) The angle subtended by the diameter of a semi-circle is

(A) 90

(B) 45

(D) 60

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Q12) If AB and CD are two chords of a circle intersecting at point E, as per the given figure. Then

(A) ∠BEQ > ∠CEQ

(B) ∠BEQ = ∠CEQ

(D) None of the above

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Q13) If a line intersects two concentric circles with centre O at A, B, C and D, then

(A) AB = CD

(B) AB > CD

(D) None of the above

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Q14) In the below figure, the value of ∠ADC is

(A) 60°

(B) 30°

(D) 55°

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Q15) In the given figure, find angle OPR.

(A) 20°

(B) 15°

(D) 10°

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Q16) In the given figure, BOC is a diameter of a circle with centre O. If AB and CD are two chords such that AB || CD and AB = 10 cm, then CD =

(A) 5 cm

(B) 12.5 cm

(D) 10 cm

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Q17) In the given figure, AB is a chord of a circle with centre O and AB is produced to C such that BC = OB. Also, CO is joined and produced to meet the circle in D. If ∠ACD = 25°, then ∠AOD =

(A) 50°

(B) 75°

(D) 100°

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Q18) In the given figure, AB is a chord of a circle with centre O and BOC is a diameter. If OD ⊥ AB such that OD = 6 cm, then AC =

(A) 9 cm

(B) 12 cm

(D) 7.5 cm

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Q19) An equilateral triangle of side 9 cm is inscribed a circle. The radius of the circle is

(A) 3 cm

(B) 3√2 cm

(D) 6 cm

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Q20) In the given figure, ΔABC and ΔDBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 50°. then, ∠BCD =

(A) 50°

(B) 60°

(D) 80°

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Q21) In the given figure, O is the centre of a circle. If ∠AOB = =100° and ∠AOC = 90°, then ∠BAC =

(A) 85°

(B) 80°

(D) 75°

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Q22) In the given figure, O is the centre of a circle and ∠AOC = 120°. Then, ∠BDC =

(A) 60°

(B) 45°

(D) 15°

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Q23) In the given figure, O is the centre of a circle in which ∠OAB = 20° and ∠OCB = 50°. Then, ∠AOC =

(A) 50°

(B) 70°

(D) 60°

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Q24) In the given figure, O is the centre of a circle in which ∠AOC = 100° side AB of quadrilateral OABC has been produced to D. Then, ∠CBD =

(A) 50°

(B) 40°

(D) 80°

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Q25) In the given figure, O is the centre of a circle and ∠OAB = 50°. Then, ∠BOD =

(A) 130°

(B) 50°

(D) 80°

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Q26) In the given figure, ABCD is the cyclic quadrilateral in which BC = CD and ∠CBD = 35°. Then, ∠BAD =

(A) 65°

(B) 70°

(D) 90°

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Q27) In figure, ΔABC is an equilateral triangle and ABDC is a quadrilateral then ∠BDC =

(A) 90°

(B) 60°

(D) 150°

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Q28) In figure, sides AB and AD of a quadrilateral ABCD are produced to E and F respectively. If ∠CBE = 100°, then find ∠CDF.

(A) 100°

(B) 80°

(D) 90°

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Q29) In figure, O is the centre of a circle and ∠AOB = 140°, then ∠ACB =

(A) 70°

(B) 80°

(D) 40°

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9th Class - Math | Chapter: Circles MCQs

Q1) The radius of a circle is 13 cm and the length of one of its chords is 10 cm. The distance of the chord from the centre is

Q2) A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. The length of the chord is

Q3) In the given figure, BOC is a diameter of a circle and AB = AC. Then, ∠ABC =

Q4) In the given figure, O is the centre of a circle. If ∠OAB = 40° and C is a point on the circle, then ∠ACB =

Q5) AB and CD are two equal chords of a circle with centre O such that ∠AOB = 80°, then ∠COD =

Q6) The center of the circle lies in______ of the circle.

Q7) The longest chord of the circle is

Q8) Equal _____ of the congruent circles subtend equal angles at the centers.

Q9) If chords AB and CD of congruent circles subtend equal angles at their centres, then:

Q10) If there are two separate circles drawn apart from each other, then the maximum number of common points they have

Q11) The angle subtended by the diameter of a semi-circle is

Q12) If AB and CD are two chords of a circle intersecting at point E, as per the given figure. Then

Q13) If a line intersects two concentric circles with centre O at A, B, C and D, then

Q14) In the below figure, the value of ∠ADC is

Q15) In the given figure, find angle OPR.

Q16) In the given figure, BOC is a diameter of a circle with centre O. If AB and CD are two chords such that AB || CD and AB = 10 cm, then CD =

Q17) In the given figure, AB is a chord of a circle with centre O and AB is produced to C such that BC = OB. Also, CO is joined and produced to meet the circle in D. If ∠ACD = 25°, then ∠AOD =

Q18) In the given figure, AB is a chord of a circle with centre O and BOC is a diameter. If OD ⊥ AB such that OD = 6 cm, then AC =

Q19) An equilateral triangle of side 9 cm is inscribed a circle. The radius of the circle is

Q20) In the given figure, ΔABC and ΔDBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 50°. then, ∠BCD =

Q21) In the given figure, O is the centre of a circle. If ∠AOB = =100° and ∠AOC = 90°, then ∠BAC =

Q22) In the given figure, O is the centre of a circle and ∠AOC = 120°. Then, ∠BDC =

Q23) In the given figure, O is the centre of a circle in which ∠OAB = 20° and ∠OCB = 50°. Then, ∠AOC =

Q24) In the given figure, O is the centre of a circle in which ∠AOC = 100° side AB of quadrilateral OABC has been produced to D. Then, ∠CBD =

Q25) In the given figure, O is the centre of a circle and ∠OAB = 50°. Then, ∠BOD =

Q26) In the given figure, ABCD is the cyclic quadrilateral in which BC = CD and ∠CBD = 35°. Then, ∠BAD =

Q27) In figure, ΔABC is an equilateral triangle and ABDC is a quadrilateral then ∠BDC =

Q28) In figure, sides AB and AD of a quadrilateral ABCD are produced to E and F respectively. If ∠CBE = 100°, then find ∠CDF.

Q29) In figure, O is the centre of a circle and ∠AOB = 140°, then ∠ACB =

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Chapters (Math)