01 · CBSE BOARD EXAM 2024
CBSE 2024 Board Practice Questions
CBSE 2024 · 1 MARK
Q1. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Find the length of PQ.
CBSE 2024 · 1 MARK
Q2. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°, then find ∠POA.
CBSE 2024 · 2 MARKS
Q3. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
CBSE 2024 · 3 MARKS
Q4. Prove that the lengths of tangents drawn from an external point to a circle are equal (Theorem 10.2).
CBSE 2024 · 5 MARKS
Q5. Prove that a parallelogram circumscribing a circle is a rhombus.
02 · CBSE BOARD EXAM 2023
CBSE 2023 Board Practice Questions
CBSE 2023 · 1 MARK
Q6. If the angle between two radii of a circle is 130°, the angle between the tangents at the ends of the radii is:
(A) 50° (B) 90° (C) 40° (D) 60°
CBSE 2023 · 2 MARKS
Q7. Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
CBSE 2023 · 3 MARKS
Q8. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
CBSE 2023 · 5 MARKS
Q9. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
03 · CBSE BOARD EXAM 2022
CBSE 2022 Board Practice Questions
CBSE 2022 · 1 MARK
Q10. If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then find ∠PTQ.
CBSE 2022 · 2 MARKS
Q11. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
CBSE 2022 · 3 MARKS
Q12. A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
04 · CBSE BOARD EXAM 2021
CBSE 2021 Board Practice Questions
CBSE 2021 · 1 MARK
Q13. If a pair of tangents are drawn from an external point P to a circle of radius a with centre O and the angle between the tangents is 60°, find the length of OP.
CBSE 2021 · 2 MARKS
Q14. Prove that the line segment joining the points of contact of two parallel tangents to a circle passes through the centre.
CBSE 2021 · 3 MARKS
Q15. If PA and PB are tangents to a circle from an external point P and MN is another tangent touching the circle at C and intersecting PA and PB at M and N respectively, prove that perimeter of △PMN = 2 PA.
05 · CBSE BOARD EXAM 2020
CBSE 2020 Board Practice Questions
CBSE 2020 · 1 MARK
Q16. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
CBSE 2020 · 3 MARKS
Q17. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact (Theorem 10.1).
CBSE 2020 · 5 MARKS
Q18. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
06 · SELF-PRACTICE TIPS
Tips for Solving Board PYQs
01
Always use Theorem 10.1 (Radius ⊥ Tangent) to form right-angled triangles and apply Pythagoras theorem.
02
Use Theorem 10.2 (Equal tangent lengths) to label tangent segments from vertices in circumscribed polygons.
03
Remember that the angle at centre and angle between external tangents are supplementary (sum = 180°).