Circles: Class 10 Previous Year Questions

Circles questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. In the given figure, PA is a tangent from an external point P to a circle with centre O. If Z POB = 125°, then Z APO is equal to : 25° (a) (b) 65° 125° :06 (c) (d)35°
   Board 20261 markMCQRepeated: 2024,2025,2026
2. In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If NML = 30 , then RLM is : (A) 30 (B) 60 (C) 90 (D) 120
   Board 20251 markMCQRepeated: 2024,2025,2026
3. In the given figure, AT is tangent to a circle centred at O. If ÐCAT = 40°, then ÐCBA is equal to 1 (A) 70° (B) 50° (C) 65° (D) 40°
   Board 20241 markMCQRepeated: 2024,2025,2026
4. A chord of a circle of radius 14 cm subtends an angle of 60°at the centre. Find the area of the corresponding minor segment of the circle. Also find the area of the major segment of the circle.
   Board 20235 markslong answerRepeated: 2023,2024,2026
5. In given figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to (a) 4 cm (b) 2 cm (c) 2√3 cm (d) 4√3 cm
   CBSE practice 2023-241 markMCQRepeated: 2024,2025,2026
6. If TP and TQ are two tangents to a circle with centre O from an external point T so that Z POQ = 120°, then Z PTQ is equal to : (b) 70° (c) 80° (a) 60° (d) 90°
   Board 20261 markMCQRepeated: 2025,2026
7. The coordinates of the centre of a circle are (x - 7, 2x). Find the value(s) of ·x', if the circle passes through the point (- 9, 11) and has radius 5/2 units. 24
   Board 20262 marksshort answerRepeated: 2025,2026
8. In the given figure, PA and PB are tangents to a circle centred at O. If Z OAB = 15°, then Z APB equals : (A) (B) 30° 15° (C) 45° (D) 10° 14. ABA0B=130° Z APB T HT : 0 6130° 130° (B) (A) 50° (C) 120° (D) :06 15. (A) 2·r (B) (C) 2·r (D) r2 sin 600 16. 1 6 1(cm3…
   Board 20261 markMCQRepeated: 2024,2026
9. In the given figure, PA and PB are tangents to a circle centred at O. If Z AOB = 130°, then Z APB is equal to : 06130° (B) 130° (A) 50° (C) 120° (D) .06
   Board 20261 markMCQRepeated: 2024,2026
10. Two concentric circles are of radi 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.
    Board 20262 marksshort answerRepeated: 2022,2026
11. If a sector of a circle has an area of 40 sq. units and a central angle of 72 , the radius of the circle is : (A) 200 units (B) 100 units (C) 20 units (D) 10 2 units
    Board 20251 markMCQRepeated: 2025,2026
12. In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular to each other. If PA = 5 cm, then length of AB is equal to 1 (A) 5 cm (B) 5 2 cm (C) 2 5 cm (D) 10 cm
    Board 20241 markMCQRepeated: 2024,2026
13. Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
    Board 20221 markvery shortRepeated: 2022,2026
14. (a) Prove that the lengths of tangents drawn from an external point to a circle are equal. OR (b) Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that Z PTQ = 2 Z OPQ.
    Board 20263 marksshort answer
15. (A) In the given figure, · ABC is a right triangle in Find the radius of the circle inscribed in the triangle ABC. OR (B) In the given figure, if a circle touches the side QR of · PQR at S and extended sides PQ and PR at M and N respectively, then prove that :…
    Board 20263 marksshort answer
16. A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors as shown in figure. Based on the above information, answer the following questions : …
    Board 20264 marksshort answer
17. The tangents drawn at the extremities of the diameter of a circle are always : (A) parallel (B) perpendicular (C) equal (D) intersecting
    Board 20251 markMCQ
18. The coordinates of the end points of a diameter of a circle are (5, 2) and (5, 2). The length of the radius of the circle is : (A) ± 2 (B) ± 4 (C) 4 (D)
    Board 20251 markMCQ
19. At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the length of the chord CD parallel to XY at a distance of 16 cm from A.
    Board 20252 marksshort answer
20. (a) Prove that the parallelogram circumscribing a circle is a rhombus. OR (b) 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 th…
    Board 20253 marksshort answer

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