CBSE Class 9 Mathematics Circle Assignment Set A

1 AB is a chord of a circle wit h centre 0 and radius 17 cm. lf OM ⊥ AB and OM = 8 cm, find the length of chord AB.
(A) 12 cm
(B) 30 cm
(C) 15 cm
(D) 24 cm
Answer : B

2 AB is a chord of length 24 cm of a circle with centre 0 and radius 13 cm. Find the distance of the chord from the centre.
(A) 5 cm
(B) 6 cm
(C) √407 cm
(D) 25 cm
Answer : A

3 48 em long chord of a circle is at a distance of 7 em from the centre. Find the radius of the circle.
(A) 5 cm
(B) 17 cm
(C) 25 cm
(D) 16 cm
Answer : C

4 A chord of a circle is 12 cm in length and its distance from the centre is 8 cm. Find the length of the chord of the same circle which is at a distance of 6 em from the centre.
(A) 30 cm
(B) 24 cm
(C) 16 cm
(D) 18 cm
Answer : C

5 In the given figure, ΔABC is inscribed in a circle with centre O. lf ∠ACB = 65°, find ∠ABC.

(A) 25°
(B) 35°
(C) 90°
(D) 65°
Answer : A

6 An equilateral ΔPQR is inscribed in a circle with centre 0. Find ∠QOR.
(A) 60°
(B) 120°
(C) 30°
(D) 90°
Answer : B

7 In the given figure, ΔXYZ is inscribed in a circle wit h centre O. lf the length of the chord YZ is equal to the radius of the circle OY, find the measure of ∠YXZ.

(A) 45°
(B) 35°
(C) 60°
(D) 55°

Answer 7: B

Answer 8: C

Answer 9: B

10 What is the least number of noncollinear points required t o draw a circle passing through them?
(A) Two
(B) Three
(C) Four
(D) Nine
Answer : B

11 Two chords AB and CD of a circle cut each other when produced outside the circle at P. AD and BC are joined. If ∠BAD= 30° and ∠CPA = 45°, find ∠CBP.

(A) 105°
(B) 115°
(C) 135°
(D) 75°
Answer : A

12 In the given figure, ΔABC is inscribed in a circle. The bisector of ∠BAC meets BC at D and t he circle at E. If EC is joined and ∠ECD = 30°, find ∠BAC.

(A) 90°
(B) 42°
(C) 48°
(D) 38°

Answer 12: D

Answer 13: C

14 The circumference of a circle is 60 cm. An arc subtends 90° at the centre. Find its length.
(A) 10 cm
(C) 20 cm
(B) 15 cm
(D) 25 cm
Answer : B

15 Two circles intersect in A and B. Quadrilaterals PCBA and ABDE are inscribed in these circles such that PAE and CBD are line segments. If ∠P is 95° find the value of z.

(A) 65°
(B) 105°
(C) 95°
(D) 85°
Answer : D

16 A circle is divided into 12 equal parts.
What is the measure of central angle in each arc?
(A) 30°
(B) 60°
(C) 45°
(D) 48°
Answer : A

17 In a circle, the major arc is twice the minor arc. What are the corresponding central angles and the degree measures of the two arcs?
(A) 90° and 270°
(B) 60° and 300°
(C) 240° and 120°
(D) 140° and 220°
Answer : C

18 In the given figure,ABCD is a quadrilateral inscribed in a circle. Diagonals AC and BD are drawn. If ∠CAD = 40° and ∠BDC = 25°, find ∠BCD.

(A) 85°
(B) 120°
(C) 115°
(D) 95°
Answer : C

19 A circle with radius 2 units is intersected by a line at points R and T. Find the maximum possible distance between R andT.
(A) 1 unit
(B) 2 n unit s
(C) 4 n unit s
(D) 4 units
Answer : D

Answer 20: D

Answer 21: C

Answer 22: D

Answer 23: A

Answer 24: D

Answer 25: A

Answer 26: C

Answer 27: A

Answer 28: B

29 Given two concentric circles with centre 0. A line cuts the circles at A, B, C and D respectively. If AB == 10 cm, find the length of CD.
(A) 5 cm
(B) 10 cm
(C) 7.5 cm
(D) 15 cm
Answer : B

30 A chord of a circle divides the circular region into two parts. What is the region that contains the centre?
(A) Minor Arc
(B) Major Arc
(C) Minor Segment
(D) Major Segment
Answer : D

31 In the given figure, find the value of y.

(A) 35 °
(B) 60° + X0
(C) 60° - X0
(D) 120°
Answer : C

32 An equilateral ΔABC is inscribed in a circle with centre 0. Find the measure of ∠BOC.
(A) 110°
(B) 100°
(C) 120°
(D) 130°
Answer : C

33 In the given figure, ABDC is a cyclic quadrilateral and AB = AC If ∠ACB = 70°, find ∠BDC.

(A) 1 00°
(B) 70°
(C) 140°
(D) 40°
Answer : C

34 When are two circles said to be concentric?
(A) If they have the same radius.
(B) If they have different radii.
(C) If they have the same centre.
(D) If their centres are collinear.
Answer : C

35 In the given figure, PaR = SRQ.

Which of the following is correct?
(A) PQ ≠ SR
(B) PS = QR
(C) PQ = SR
(D) PS ≠ QR 
Answer : C

36 is the centre of a circle, ∠BOA = 90° and ∠COA = 110°. Find the measure of ∠BAC.
(A) 70 °
(B) 80°
(C) 120°
(D) 50°
Answer : B

37 In the given figure, 0 is the centre of the circle, OM ⊥ BC, OL ⊥ AB, ON ⊥ AC and OM = ON = OL. What is ΔABC?

(A) Right angled triangle
(B) Scalene triangle
(C) Isosce les triangle
(D) Equilateral triangle
Answer : D

38 In the given figure, 0 is the centre of a circle having radius 5 cm.lf OM ⊥ PQ and OM = 3 em, find the length of chord PQ.

(A) 5 cm
(B) 8 cm
(C) 10 cm
(D) 6 cm
Answer : B

Answer 39: D

Answer 40: D

Answer 41: A

Answer 42: C

Answer 43: D

Answer 44: C

Answer 45: A

Answer 46: A

Answer 47: C

Answer 48: C

Answer 49: B

Answer 50: D

Circles

Q 1 True or False: It is possible to draw two circles passing through three given non-collinear points.

Q 2 State the following statement as true or false. Give reasons also.The perpendicular bisector of two chords of a circle intersect at centre of the circle.

Q 3 True or False :
If two arcs of a circle are congruent, then corresponding chords are unequal.

Q 4 State the following statement as true or false . Give reasons also.
Line segment joining the centre to any point on the circle is a radius of the circle.

Q 5 O is the centre of a circle of radius 5 cm. OP ⊥AB and OQ ⊥CD, AB || CD, AB = 6 cm and CD = 8 cm. Determine PQ.

Q 6 In figure, O is the centre of a circle and ∠ADC=1200. Find ∠BAC.

Q 7 In Figure, △ABC is equilateral . Find ∠ABC ∠AEC.

Click on link below to download CBSE Class 9 Mathematics Circle Assignment Set A