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CBSE Class 9 Mathematics Worksheet

Unit 4-Geometry - Circles

In the given figure BD = DC and $\angle DBC = 15^{\circ}$ . Find $\angle A$ .

60°

30°

45°

75°

In the given figure, chord AB is at a distance 6cm from centre O. If the AB = 16cm, find the radius of the circle.

A) 20 cm B) 8 cm C) 10 cm D) 5 cm

State True/False: A circle is a solid figure.

A) True B) False

Choose the correct option: If AB = 12 cm, BC = 5 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is ________.

A) 5.5 cm B) 13 cm C) 6.5 cm D) 12 cm

In the given figure, AH, DH, BF and CF are the bisectors of A, D, B and C respectively. Then EFGH is a _______.

A) Square B) Rectangle C) Any Parallelogram D) None of these

In the given figure, O is the centre of the circle. Find $\angle BDO$ .

60°

30°

45°

75°

State True/False: If chords of congruent circles subtend equal angles at their centres, then the chords are equal.

A) True B) False

If AOB is a diameter of the circle and AC = BC = 4cm, then find the length of AB.

A) $4\sqrt{2}cm$ B) 8 cm C) $4\sqrt{2}$ D) 4 cm

In the given figure, AB is a diameter of the circle C and the radius OD is perpendicular to AB. If C is any point on , then $\angle BAD$ is_________.

A) $35^{\circ}$ B) $35^{\circ}$ C) $35^{\circ}$ D) $35^{\circ}$

10.

Choose the correct option: If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral. Then the quadrilateral is __________.

A) Square B) Rectangle C) Any parallelogram D) Rhombus

11.

State True/False: There is one and only one circle passing through three non-collinear points.

A) True B) False

12.

In the given figure, $\angle PQR = 100^{\circ}$ , where P, Q and R are points on a circle with centre O. Find $\angle OPR$ .

A) $30^{\circ}$ B) $30^{\circ}$ C) $30^{\circ}$ D) $30^{\circ}$

13.

In the given A, B, C and D are four points on a circle. AC and BD intersect at a point E such that $\angle BEC = 130^{\circ}$ and $\angle ECD = 20^{\circ}$ . Find $\angle BAC$ .

A) $110^{\circ}$ B) $110^{\circ}$ C) $110^{\circ}$ D) $110^{\circ}$

14.

Fill in the blanks: When the ends of an arc is are the ends of a diameter then it is called ________.

A) circle B) major arc C) semi circle D) None of these

15.

In the given figure, chord ED is parallel to the diameter AC of the circle. If $\angle CBE = 65^{\circ}$ , then the value of $\angle DEC$ is ______.

A) $15^{\circ}$ B) $15^{\circ}$ C) $15^{\circ}$ D) $15^{\circ}$

16.

In the given figure $\angle ABC = 42.5^{\circ}$ . Find $\angle AOC$ .

65°

85°

95°

90°

17.

In the given figure, the bisector of B of an isosceles triangle ABC with AB = AC meets the circumcircle of ABC at P. If AP and BC produced meet at Q. Then which of the following is true?

A) AP = PB B) CQ = CA C) AP = AB D) None of these

18.

In the given figure, AB is the diameter of the circle. If C is a point on the circle such that $\angle ADC = 60^{\circ}$ , then $\angle BAC$ is ______.

A) $15^{\circ}$ B) $15^{\circ}$ C) $15^{\circ}$ D) $15^{\circ}$

19.

State True/False: Congruent arcs of a circle subtend equal angles at the centre.

A) True B) False

20.

In the given figure $\angle BAC = 60^{\circ}$ , $\angle CBA = 70^{\circ}$ , find $\angle BDA$ .

A) $30^{\circ}$ B) $30^{\circ}$ C) $30^{\circ}$ D) $30^{\circ}$

CBSE Class 9 Mathematics Worksheet

Unit 4-Geometry - Circles

Answers

Option B

Option C

Option B

Option C

Option D

Option A

Option D

10.

Option B

11.

Option A

12.

Option C

13.

Option A

14.

Option C

15.

Option C

16.

Option B

17.

Option B

18.

Option B

19.

Option A

20.

Option C

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