CBSE BOARD PYQS · CHAPTER 10

Circles
CBSE Most Repeated PYQs

Solve official CBSE Previous Year Board Questions (2015-2024) for Circles. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.

Q1CBSE 2024, 2020MCQ

1 Mark

Tangent PT at point P of circle of radius 5 cm meets line through centre O at point T so OT = 12 cm. Length PT is:

Q2CBSE 2023, 2019MCQ

1 Mark

From point Q, length of tangent to circle is 24 cm and distance of Q from centre is 25 cm. Radius is:

Q3CBSE 2022, 2018MCQ

1 Mark

If TP and TQ are two tangents to circle with centre O so that ∠POQ = 110°, then ∠PTQ is:

Q4CBSE 2024, 2021MCQ

1 Mark

If tangents PA and PB from point P to circle with centre O are inclined to each other at angle 80°, then ∠POA is:

Q5CBSE 2023, 2017Assertion-Reason

1 Mark

Assertion (A): The tangent at any point of a circle is perpendicular to the radius through the point of contact. Reason (R): Length of tangents drawn from an external point to a circle are equal.

Q6CBSE 2020, 2016Assertion-Reason

1 Mark

Assertion (A): A circle can have infinitely many tangents. Reason (R): A tangent intersects a circle at exactly one point.

Q7CBSE 2024, 2020Short Answer

2 Marks

Prove that tangents drawn at the ends of a diameter of a circle are parallel.

Q8CBSE 2023, 2019Short Answer

2 Marks

Prove that perpendicular at point of contact to tangent to circle passes through centre.

Q9CBSE 2022, 2018Short Answer

2 Marks

Two concentric circles are of radii 5 cm and 3 cm. Find length of chord of larger circle which touches smaller circle.

Q10CBSE 2024, 2021Short Answer

2 Marks

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

Q11CBSE 2023, 2017Short Answer

2 Marks

Prove that parallelogram circumscribing a circle is a rhombus.

Q12CBSE 2020, 2016Long Answer

3 Marks

Prove that lengths of tangents drawn from an external point to a circle are equal.

Q13CBSE 2024, 2020Long Answer

3 Marks

Triangle ABC is drawn to circumscribe circle of radius 4cm such that segments BD and DC are 8cm and 6cm. Find sides AB and AC.

Q14CBSE 2023, 2019Long Answer

3 Marks

Prove that angle between two tangents from external point is supplementary to angle subtended by segment joining points of contact.

Q15CBSE 2022, 2018Long Answer

3 Marks

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at center.

Q16CBSE 2024, 2021Case Study

4 Marks

Case Study Scenario: A round clock has tangents drawn from point P outside. PA = 12 cm and P is 13 cm from center O. Question: Find radius of clock and area of quadrilateral OAPB.

Q17CBSE 2023, 2017Case Study

4 Marks

Case Study Scenario: A circular park is circumscribed by quadrilateral ABCD. Question: If AB = 6 cm, BC = 7 cm, CD = 4 cm, find AD.

Q18CBSE Official Board PYQPYQ

5 Marks

In figure, XY & X'Y' are parallel tangents. Tangent AB with point of contact C intersects XY at A & X'Y' at B. Prove ∠AOB = 90°.

Q19CBSE Official Board PYQPYQ

5 Marks

PQ is chord of length 8 cm of circle of radius 5 cm. Tangents at P and Q intersect at T. Find length TP.

Q20CBSE Official Board PYQPYQ

5 Marks

Circles CBSE Most Repeated PYQs

Tangent PT at point P of circle of radius 5 cm meets line through centre O at point T so OT = 12 cm. Length PT is:

From point Q, length of tangent to circle is 24 cm and distance of Q from centre is 25 cm. Radius is:

If TP and TQ are two tangents to circle with centre O so that ∠POQ = 110°, then ∠PTQ is:

If tangents PA and PB from point P to circle with centre O are inclined to each other at angle 80°, then ∠POA is:

Assertion (A): The tangent at any point of a circle is perpendicular to the radius through the point of contact. Reason (R): Length of tangents drawn from an external point to a circle are equal.

Assertion (A): A circle can have infinitely many tangents. Reason (R): A tangent intersects a circle at exactly one point.

Prove that tangents drawn at the ends of a diameter of a circle are parallel.

Prove that perpendicular at point of contact to tangent to circle passes through centre.

Two concentric circles are of radii 5 cm and 3 cm. Find length of chord of larger circle which touches smaller circle.

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

Prove that parallelogram circumscribing a circle is a rhombus.

Prove that lengths of tangents drawn from an external point to a circle are equal.

Triangle ABC is drawn to circumscribe circle of radius 4cm such that segments BD and DC are 8cm and 6cm. Find sides AB and AC.

Prove that angle between two tangents from external point is supplementary to angle subtended by segment joining points of contact.

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at center.

Case Study Scenario: A round clock has tangents drawn from point P outside. PA = 12 cm and P is 13 cm from center O. Question: Find radius of clock and area of quadrilateral OAPB.

Case Study Scenario: A circular park is circumscribed by quadrilateral ABCD. Question: If AB = 6 cm, BC = 7 cm, CD = 4 cm, find AD.

In figure, XY & X'Y' are parallel tangents. Tangent AB with point of contact C intersects XY at A & X'Y' at B. Prove ∠AOB = 90°.

PQ is chord of length 8 cm of circle of radius 5 cm. Tangents at P and Q intersect at T. Find length TP.

Two tangents TP and TQ are drawn to circle with centre O from external point T. Prove ∠PTQ = 2 ∠OPQ.

Circles
CBSE Most Repeated PYQs