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. Prove that the tangent drawn at any point of the circle is perpendicular to the radius through the point of contact.
   Board 20252 marksshort answerRepeated: 2022,2025
2. | P a g e 25. A chord of a circle of diameter 20 cm subtends an angle of 60 at the centre of the circle. Find the area of the corresponding minor segment of the circle. (Use = 3·14 and = 1·73) 16| P a g e 6 - (SA) , 3 6 3=18 26. x x, y, a b x 27. 0 9 28. x + 3…
   Board 20252 marksshort answerRepeated: 2024,2025
3. A chord of a circle of radius 14 cm subtends an angle of 90° at the centre. Find the area of the corresponding minor and major segments of the circle.
   Board 20245 markslong answerRepeated: 2024,2025
4. (a) Prove that a parallelogram circumscribing a circle is a rhombus. OR (b) Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.
   Board 20221 markvery shortRepeated: 2022,2025
5. Two concentric circles are of radii 6 cm and 10 cm. Find the length of the chord of the larger circle which touches the smaller circle.
   Board 20252 marksshort answer
6. In the given figure, PA is a tangent to a circle with centre O. If OP = 10 cm, then the length of AP is : (A) 10 cm (B) 20 cm (C) 5 cm (D) 5 cm
   Board 20251 markMCQ
7. | P a g e 25. (a) The area of a smaller circle is equal to the area of a sector of a larger circle with central angle 120 . The radii of the smaller and . OR (b) In the given figure, O is the centre of a circle of radius 7 cm. AB is a chord of the circle. Find…
   Board 20252 marksshort answer
8. In the given figure, TP and TQ are tangents at points P and Q of the circle respectively. If reflex POQ = 250 , find the measure of each angle of quadrilateral POQT.
   Board 20253 marksshort answer
9. | P a g e 37. In a garden, saplings of rose flowers were planted at equal intervals to form a spiral pattern. The spiral is made up of successive semicircles, with centres alternatively at A and B, starting with centre at A, of radii 50 cm, 100 cm, 150 cm, ...…
   Board 20254 marksshort answer
10. | P a g e 14. The ratio of the area of a quadrant of a circle to the area of the same circle is : (A) 1 : 2 (B) 2 : 1 (C) 1 : 4 (D) 4 : 1 10| P a g e 15. ? (A) (B) (C) (D) 16. - - 10 25 25 40 40 55 55 70 70 85 85 100 2 3 7 6 6 6 (A) 40 (B) 55 (C) 47·5 (D) 62·5…
    Board 20251 markMCQ
11. (A) In two concentric circles, the radii are OA = r cm and OQ = 6 cm, as shown in the figure. Chord CD of larger circle is a tangent to smaller circle at Q. PA is tangent to larger circle. If PA = 16 cm and OP = 20 cm, find the length CD. C3ABD/1 /31 Page 9 ZP…
    Board 20243 marksshort answer
12. In the given figure, tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°. ÐABO is equal to 1 (A) 40° (B) 80° (C) 100° (D) 50°
    Board 20241 markMCQ
13. Prove that the tangents drawn at the ends of a diameter of a circle are parallel to each other.
    Board 20242 marksshort answer
14. Assertion (A) : If the PA and PB are tangents drawn to a circle with centre O from an external point P, then the quadrilateral OAPB is a cyclic quadrilateral. Reason (R) : In a cyclic quadrilateral, opposite angles are equal.
    Board 20241 markAssertion-Reason
15. The picture given below shows a circular mirror hanging on the wall with a cord. The diagram represents the mirror as a circle with centre O. AP and AQ are tangents to the circle at P and Q respectively such that AP = 30 cm and ZPAQ= 60°. Based on the above in…
    Board 20244 marksshort answer
16. A line intersecting a circle in two distinct points is called a 1 (A) secant (B) chord (C) diameter (D) tangent
    Board 20241 markMCQ
17. Prove that the tangents drawn from an external point to a circle are equal in length.
    Board 20233 marksshort answer
18. From a point P, two tangents PQ and PR are drawn to a circle with centre at O. T is a point on the major arc QR of the circle. If QPR = 50 , then QTR equals : (a) 50 (b) 130 (c) 65 (d) 90
    Board 20231 markMCQ
19. The distance between two parallel tangents of a circle of diameter 7 cm is : 7 cm (a) (b) 14 cm (c) (d) 2cm 28 cm
    Board 20231 markMCQ
20. Interschool Rangoli Competition was organized by one of the reputed schools of Odissa. The theme of the Rangoli Competition was Diwali celebrations where students were supposed to make mathematical designs. Students from various schools participated and made b…
    Board 20234 marksshort answer

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