Skip to content

Radius r of the… (Class 10 Maths Basic SQP 2025-26, Q11)

questionbuddy.in/q/cbse-10-maths-2025-26-sqp-basic-q11-radius-circle-touches-sides-triangle

MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 11

From the official CBSE sample question paper for 2025-26, section A, question 11, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q11 · 1 mark · MCQCircles

In the figure given below, radius of the circle which touches the sides of the triangle is

  1. (A)3 cm
  2. (B)6 cm
  3. (C)7 cm
  4. (D)4 cm

Figure in the paper: Right-angled triangle ABC with right angle at C. Side AC (vertical) = 24 cm, base BC (horizontal) = 7 cm, hypotenuse AB = 25 cm. A circle with centre O and radius r touches all three sides at D (on BC), E (on AC) and F (on AB); radii OD, OE and OF are marked r. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Tangents drawn from the same point are equal.

Hint 2

Express AF and BF in terms of .

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. OECD is a square of side [tangent ⟂ radius, ]. So .

  2. Tangents from an external point are equal: and .

  3. : cm, option (A).

    1 mark

Answer: 3 cm, option (A)

Where the marks are

  • Uses equal tangents to get , so cm (1 mark)

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 paperSample paper 2025-26 (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.