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A chord of a circle of… (Class 10 Maths Basic 2025, Q25)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 25

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerAreas Related to Circles

A chord of a circle of diameter 20 cm subtends an angle of at the centre of the circle. Find the area of the corresponding minor segment of the circle. (Use and )

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Minor segment = sector − triangle formed by the chord and the two radii.

Hint 2

With a angle between two equal radii, the triangle is equilateral, so its area is .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. Radius cm. Let chord PQ subtend at O. Since and , is equilateral.

    ½ mark

  2. Area of minor segment = area of sector − area of

    1 mark

  3. cm² cm²

    ½ mark

Answer: 109/12 cm² ≈ 9.08 cm²

Where the marks are

  • Takes cm and recognises as equilateral (½ mark)
  • Writes area of segment = sector − triangle with correct substitution (1 mark)
  • Gets cm² (½ mark)

Revise the chapter

Practise this chapterBoard-style questions from Areas Related to Circles, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/1/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.