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Δ ABC is a right triangle in… (Class 10 Maths 2026, Q29A)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 29(A)

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section C, question 29(A), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(A) · 3 marks · Short answerCircles

In the given figure, ABC is a right triangle in which B = , AB = 4 cm and BC = 3 cm. Find the radius of the circle inscribed in the triangle ABC.

Figure in the paper: Right triangle ABC with right angle at B (bottom right). A is at the top, C at bottom left, B at bottom right. A circle is inscribed inside the triangle touching all three sides. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

Hints

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

Hint 1

First find the hypotenuse AC.

Hint 2

Tangents drawn from a vertex to the incircle are equal. Let the tangent length from B be x.

Hint 3

Add the tangent lengths from A and C to get AC. Since ∠B = 90°, the tangent length from B equals the radius.

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. In right , .

    By Pythagoras theorem, cm.

    ½ mark

  2. Let the incircle (centre O) touch AB at D, BC at E and CA at F. Let cm [tangents from an external point are equal].

    ½ mark

  3. Then and [tangents from A and from C are equal].

    ½ mark

  4. Since :

    1 mark

  5. In quadrilateral ODBE, , [tangent ⟂ radius] and . So ODBE is a square, and radius cm.

    Hence the radius of the inscribed circle is 1 cm.

    ½ mark

Answer: Radius = 1 cm

Where the marks are

  • Finds AC = 5 cm (½ mark)
  • Takes BD = BE = x using equal tangents (½ mark)
  • Writes AD = AF = 4 − x and CE = CF = 3 − x (½ mark)
  • Forms (4 − x) + (3 − x) = 5 and gets x = 1 (1 mark)
  • Concludes radius = 1 cm, since ODBE is a square (½ mark)
  • Alternative: equating area 6 cm² with ½·r·(4 + 3 + 5) to get r = 1 cm earns full marks

Revise the chapter

  • Chapter: Circles (notes, formulas, where marks are lost and every past question)
Practise this chapterBoard-style questions from Circles, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/1/1 (Standard): 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.