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The perimeter of the… (Class 10 Maths Basic 2025, Q13)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 13

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section A, question 13, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q13 · 1 mark · MCQAreas Related to Circles

The perimeter of the shaded region in the given figure is :

  1. (A)
  2. (B)
  3. (C)
  4. (D)

Figure in the paper: A circle with centre O. A chord of length a joins two points on the circle. The shaded region is the minor segment-plus-triangle region bounded by two radii OA and OB (each labelled r), the chord AB (labelled a), and the arc AB (labelled l) on the lower side of the chord. See it in the official paper.

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

Trace only the outer boundary of the shaded region.

Hint 2

Does the chord form part of that boundary?

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. The shaded region is the sector bounded by the two radii and the arc . The chord lies inside the sector and is not part of its boundary.

  2. Perimeter . The answer is option (C).

    1 mark

Answer: l + 2r, option (C)

Where the marks are

  • Perimeter of the sector = l + 2r (1 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.