Skip to content

In two concentric… (Class 10 Maths Basic 2024, Q27a)

questionbuddy.in/q/cbse-10-maths-2024-430-2-1-q27a-concentric-circles-chord-length-larger

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2024: question 27(a)

Set in the CBSE Class 10 board exam of 2024, paper 430/2/1, section C, question 27(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(a) · 3 marks · Short answerCircles

In two concentric circles, a chord of length 24 cm of larger circle touches the smaller circle, whose radius is 5 cm. Find the radius of the larger circle.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/2/1.

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 OP?

Hint 2

The perpendicular from the centre to a chord bisects the chord, so find half of 24.

Hint 3

Use Pythagoras in the right triangle formed by O, P and an end of the chord.

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: concentric circles with centre O. Chord AB of the larger circle touches the smaller circle at P. Join OP and OA, with cm.

    ½ mark

  2. [tangent ⟂ radius], and the perpendicular from the centre bisects the chord, so cm.

    1 mark

  3. In right : [Pythagoras theorem]

    1 mark

  4. cm, so the radius of the larger circle is 13 cm.

    ½ mark

Answer: 13 cm

Where the marks are

  • Correct figure (½ mark)
  • and cm (1 mark)
  • Applies Pythagoras: (1 mark)
  • Radius = 13 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 paper2024 board paper, set 430/2/1 (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.