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Two concentric circles… (Class 10 Maths Basic 2025, Q23)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 23

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerCircles

Two concentric circles are of radii 6 cm and 10 cm. Find the length of the chord of the larger circle which touches the smaller circle.

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

Hints

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

Hint 1

The chord is a tangent to the smaller circle. What angle does it make with the radius at the point of contact?

Hint 2

Use Pythagoras in the triangle formed by the centre, the point of contact and one end of the chord, then double the result.

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. Figure: two concentric circles with centre O. Chord AB of the larger circle touches the smaller circle at C. Join OC and OB. Here cm and cm.

    ½ mark

  2. [tangent ⟂ radius at the point of contact]. In right : , so cm.

    1 mark

  3. The perpendicular from the centre bisects the chord, so cm.

    ½ mark

Answer: 16 cm

Where the marks are

  • Draws a correct figure (½ mark)
  • Uses and Pythagoras to get cm (1 mark)
  • Gets cm (½ 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 430/1/1 (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.