MathsCBSE Class 10 · Basic · Board exam 2026, set 430/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 25(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/2/1, section B, question 25(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(b) · 2 marks · Very short answerAreas Related to Circles

In the given figure, O is the centre of a circle of radius 7 cm. AB is a chord of the circle. Find the perimeter of the shaded region.

Figure in the paper: Circle with centre O. Chord AB subtends a central angle of $6 0^{\circ}$ at O; OA and OB are each marked 7 cm. The shaded region is the minor segment between chord AB and the arc AB. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/2/1.

Hints

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

Hint 1

The boundary of the shaded segment is made of the chord AB and the arc AB.

Hint 2

With $O A = O B$ and a $6 0^{\circ}$ angle between them, what kind of triangle is OAB?

Hint 3

Arc length $= \frac{θ}{36 0 ^{\circ}} \times 2 π r$ .

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.

In $△ O A B$ , $O A = O B = 7$ cm and $∠ A O B = 6 0^{\circ}$ . So $∠ O A B = ∠ O B A = 6 0^{\circ}$ and the triangle is equilateral. Hence $A B = 7$ cm.
1 mark
Length of arc $A B = \frac{θ}{36 0 ^{\circ}} \times 2 π r = \frac{60}{360} \times 2 \times \frac{22}{7} \times 7 = \frac{22}{3}$ cm.
½ mark
Perimeter of the shaded segment $= A B + arc A B = 7 + \frac{22}{3} = \frac{43}{3}$ cm $\approx 14.33$ cm.
½ mark

Answer: $\frac{43}{3}$ cm ≈ 14.33 cm

Where the marks are

Shows that $△ O A B$ is equilateral, so $A B = 7$ cm (1 mark)
Finds the arc length $22/3$ cm (½ mark)
Adds them to get the perimeter $43/3$ cm (½ mark)

Revise the chapter

Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)

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 paper2026 board paper, set 430/2/1 (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.

CBSE Class 10 Mathematics Basic 2026: question 25(b)

Hints

Step-by-step solution

Revise the chapter

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