Areas Related to Circles: Class 10 Previous Year Questions

Areas Related to 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. Find the area of the sector of a circle of radius 42 cm and of central angle 22 3o°. Also, find the area of the corresponding major sector. [Use · :
   Board 20263 marksshort answerRepeated: 2023,2025,2026
2. The length of the arc of the sector of a circle with radius 21 cm and of central angle 60°, is : (a) 22 cm ¥44cm (c) 88 cm (b) (d) 11 cm
   Board 20261 markMCQRepeated: 2023,2025,2026
3. Area of a segment of a circle of radius r and central angle 60° is : (A) 2·r (B) (C) 2·r (D) r2 sin 60°
   Board 20261 markMCQRepeated: 2025,2026
4. q 32. An arc of a circle of radius 21 cm subtends an angle of 60° at the centre. Find : (i) the length of the arc. (ii) the area of the minor segment of the circle made by the corresponding chord.
   Board 20245 markslong answerRepeated: 2023,2024
5. JJJJ Page 3 2. What is the length of the arc of the sector of a circle with radius 14 cm and of central angle 90 ? (a) 22 cm (b) 44 cm (c) 88 cm (d) 11 cm JJJJ Page 4 3. `{X ABC PQR _|, A = 32 Am¡a R = 65 h¡, Vmo B H$s _mn h¡ : (a) 32 (b) 65 (c) 83 (d) 97 4. `…
   Board 20231 markMCQRepeated: 2023,2026
6. The point which lies on the perpendicular bisector of the line segment joining the points A (– 3, – 4) and B (3, 4) is: (A) (0, 0) (B) (0, 3) (C) (3, 0) (D) (0, 4)
   Sample paper 2026-271 markMCQRepeated: 2025,2026
7. | P a g e 22. (a) In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and AOB = 90 . If AO = OB = 42 cm, then find the perimeter of the top of the table. OR 14| P a g e ( ) , 5 cm , 35 , 50 95 [ = ] 23. tan A = ; …
   Board 20252 marksshort answer
8. The length of the hour hand of a clock is 10 cm. Find the area of the minor sector swept by the hour hand of the clock between 5 a.m. to 8 a.m. Also, find the area of the major sector.
   Board 20253 marksshort answer
9. (a) The diagonal BD of a parallelogram ABCD intersects the line segment AE at the point F, where E is any point on the side BC. Prove that DF EF = FB FA. OR (b) In ABC, if AD BC and AD2 = BD DC, then prove that BAC = 90 .
   Board 20255 markslong answer
10. | P a g e 37. A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from precious metals and decorated with gemstones, brooches come in many shapes and designs. One such brooch is made with silver wire in …
    Board 20254 marksshort answer
11. If a large circular pizza is divided into 5 equal sectors, then the central angle of each sector will be : (A) 60 (B) 90 (C) 45 (D) 72
    Board 20251 markMCQ
12. Page 19 35. The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector. 5 Page 20 – 3 4 36.          t     ,     h     h = 25t – 5t2   …
    Board 20245 markslong answer
13. (a) In what ratio is the line segment joining the points (3, –5) and (–1, 6) divided by the line y = x ? 2 OR (b) A(3, 0), B(6, 4) and C(–1, 3) are vertices of a triangle ABC. Find length of its median BE.
    Board 20242 marksshort answer
14. The arc of a circle is of length 6𝜋 cm and the sector it bound has an area of 24𝜋 cm2. The radius of the circle is: (A) 4 cm (B) 8 cm (C) 16 cm (D) 18 cm
    Sample paper 2026-271 markMCQ
15. Shown below is a circle with centre O. NQ is a tangent to the circle. (Note: The figure is not to scale.) Find the measure of ∠OQN. Show your work and give valid reasons.
    CBSE practice 2022-232 marksshort answer
16. Find the area of a sector of a circle with diameter 28 cm, If the length of the corresponding arc is 22 cm.
    Sample paper 2026-272 marksshort answer
17. A 3.5 cm chord subtends an angle of 60° at the centre of a circle. What is the arc length of the minor sector? Draw a rough figure and show your steps. (Note: Take π as 22 7 .) OR A semicircle MON is inscribed in another semicircle. Radius OL of the larger sem…
    CBSE practice 2022-232 marksshort answer
18. A circle with radius 6 cm is shown below. The area of the shaded region in the circle is of the area of the circle. (Note: The figure is not to scale.) What is the length of the circle's minor arc? (a) 16𝜋 3 cm (b) 20𝜋 3 cm (c) 16π cm (d) 20π cm
    CBSE practice 2023-241 markMCQ
19. A regular pentagon is inscribed in a circle with centre O, of radius 5 cm, as shown below. What is the area of the shaded part of the circle? (a) 2π cm2 1 (b) 4π cm2 (c) 5π cm2 (d) 10π cm2
    CBSE practice 2023-241 markMCQ
20. In the figure below, a unit square ROST is inscribed in a circular sector with centre O. Along with the above information, which of these is SUFFICIENT to find the area of sector POQ? A) area of the square ROST B) radius of sector POQ C) arc length PQ D) (the …
    CBSE practice 2022-231 markvery short

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