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In two concentric circles… (Class 10 Maths Basic 2025, Q13)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 13

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, section A, question 13, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q13 · 1 mark · MCQCircles

In two concentric circles centred at O, a chord AB of the larger circle touches the smaller circle at C. If OA = 3.5 cm, OC = 2.1 cm, then AB is equal to

  1. (A)5.6 cm
  2. (B)2.8 cm
  3. (C)3.5 cm
  4. (D)4.2 cm

Figure in the paper: Two concentric circles centred at O. Chord AB of the larger circle is horizontal and touches the smaller circle at C; OC is perpendicular to AB. Dashed line joins A to O. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

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

Hint 1

OC is perpendicular to AB.

Hint 2

Find AC in right triangle OCA, then double it.

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. [tangent ⟂ radius], and the perpendicular from the centre bisects the chord AB.

  2. cm, so cm.

    1 mark

Answer: 5.6 cm, option (A)

Where the marks are

  • Uses Pythagoras to get AC = 2.8 cm and doubles it to get AB = 5.6 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 paper2025 board paper, set 430/6/1 (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.