ANNUAL EXAM PYQS · CHAPTER 09

Circles
CBSE Most Repeated PYQs

Solve official Class 9 Annual Examination Questions for Circles. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.

Q1Annual Exam 2024MCQ

1 Mark

Equal chords of a circle subtend equal angles at the:

Q2Annual Exam 2023MCQ

1 Mark

Perpendicular from centre of a circle to a chord:

Q3CBSE Pattern PYQMCQ

1 Mark

Angle subtended by an arc at centre is how many times angle subtended at remaining circumference?

Q4Annual Exam 2022MCQ

1 Mark

Angles in the same segment of a circle are:

Q5CBSE Model PYQAssertion-Reason

1 Mark

Assertion (A): The sum of either pair of opposite angles of a cyclic quadrilateral is 180°. Reason (R): A quadrilateral is cyclic if all its four vertices lie on a circle.

Q6Annual Exam 2021Assertion-Reason

1 Mark

Assertion (A): Angle in a semicircle is a right angle. Reason (R): The central angle of a semicircle is 180°.

Q7Annual Exam 2024Short Answer

2 Marks

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find distance of chord from centre.

Q8Annual Exam 2023Short Answer

2 Marks

Two concentric circles have radii 5 cm and 3 cm. Find length of chord of larger circle touching smaller circle.

Q9CBSE Pattern PYQShort Answer

2 Marks

In figure, ∠AOB = 90° and ∠BOC = 120°. Find ∠ABC if A, B, C lie on circle.

Q10Annual Exam 2022Short Answer

2 Marks

ABCD is a cyclic quadrilateral. If ∠A = 70°, find ∠C.

Q11CBSE Model PYQShort Answer

2 Marks

If diagonals of a cyclic quadrilateral are diameters of circle, show it is a rectangle.

Q12Annual Exam 2021Long Answer

3 Marks

Prove that angle subtended by an arc at centre is double the angle subtended by it at any point on remaining part of circle.

Q13Annual Exam 2024Long Answer

3 Marks

Prove that sum of either pair of opposite angles of a cyclic quadrilateral is 180°.

Q14Annual Exam 2023Long Answer

3 Marks

If non-parallel sides of a trapezium are equal, prove that it is cyclic.

Q15CBSE Pattern PYQLong Answer

3 Marks

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ drawn. Prove ∠ACP = ∠QCD.

Q16Annual Exam 2022Case Study

4 Marks

Case Study Scenario: Three girls Reshma, Salma and Mandakini play a game standing on circle of radius 5m. Distance between Reshma & Salma is 6m, Salma & Mandakini is 6m. Question: Find distance between Reshma and Mandakini.

Q17CBSE Model PYQCase Study

4 Marks

Case Study Scenario: A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David sit at equal distance on its boundary. Question: Find length of string of each phone (side of equilateral triangle).

Q18Annual Exam PYQPYQ

5 Marks

In figure, ∠ABC = 69° and ∠ACB = 31°. Find ∠BDC.

Q19Annual Exam PYQPYQ

5 Marks

In figure, A, B, C, D are 4 points on circle. AC and BD intersect at E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.

Q20Annual Exam PYQPYQ

5 Marks

Circles CBSE Most Repeated PYQs

Equal chords of a circle subtend equal angles at the:

Perpendicular from centre of a circle to a chord:

Angle subtended by an arc at centre is how many times angle subtended at remaining circumference?

Angles in the same segment of a circle are:

Assertion (A): The sum of either pair of opposite angles of a cyclic quadrilateral is 180°. Reason (R): A quadrilateral is cyclic if all its four vertices lie on a circle.

Assertion (A): Angle in a semicircle is a right angle. Reason (R): The central angle of a semicircle is 180°.

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find distance of chord from centre.

Two concentric circles have radii 5 cm and 3 cm. Find length of chord of larger circle touching smaller circle.

In figure, ∠AOB = 90° and ∠BOC = 120°. Find ∠ABC if A, B, C lie on circle.

ABCD is a cyclic quadrilateral. If ∠A = 70°, find ∠C.

If diagonals of a cyclic quadrilateral are diameters of circle, show it is a rectangle.

Prove that angle subtended by an arc at centre is double the angle subtended by it at any point on remaining part of circle.

Prove that sum of either pair of opposite angles of a cyclic quadrilateral is 180°.

If non-parallel sides of a trapezium are equal, prove that it is cyclic.

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ drawn. Prove ∠ACP = ∠QCD.

Case Study Scenario: Three girls Reshma, Salma and Mandakini play a game standing on circle of radius 5m. Distance between Reshma & Salma is 6m, Salma & Mandakini is 6m. Question: Find distance between Reshma and Mandakini.

Case Study Scenario: A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David sit at equal distance on its boundary. Question: Find length of string of each phone (side of equilateral triangle).

In figure, ∠ABC = 69° and ∠ACB = 31°. Find ∠BDC.

In figure, A, B, C, D are 4 points on circle. AC and BD intersect at E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.

If circles are drawn taking two sides of a triangle as diameters, prove that their point of intersection lies on third side.

Circles
CBSE Most Repeated PYQs