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The sum of radii of two… (Class 10 Maths 2025, Q14)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 14

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section A, question 14, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q14 · 1 mark · MCQCircles

In the adjoining figure, the sum of radii of two concentric circles is 16 cm. The length of chord AB which touches the inner circle at P is 16 cm. The difference of the radii of the given circles is

  1. (A)8 cm
  2. (B)4 cm
  3. (C)2 cm
  4. (D)3 cm

Figure in the paper: Two concentric circles with centre O. Chord AB of the outer circle touches the inner circle at P, with P lying on the chord between A and B; A and B are at the ends of the chord on the outer circle. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

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

Hint 1

Triangle OPA is right-angled at P.

Hint 2

Factor .

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. OP ⟂ AB [tangent ⟂ radius], so P bisects AB: . With outer, inner: .

  2. cm. Option (B).

    1 mark

Answer: 4 cm, option (B)

Where the marks are

  • Uses and factorises to get 4 cm (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Circles, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/5/1 (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.