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Two concentric circles are of… (Class 10 Maths 2023, Q30)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 30

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section C, question 30, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30 · 3 marks · Short answerCircles

Two concentric circles are of radii 5 cm and 3 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 2023 board paper, set 30/4/1.

Hints

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

Hint 1

The chord is a tangent to the inner circle. What angle does it make with the radius OP?

Hint 2

The perpendicular from the centre bisects the chord. Use Pythagoras in triangle OPA.

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: Draw two concentric circles with centre O, of radii 5 cm and 3 cm. Draw chord AB of the larger circle touching the smaller circle at P. Join OP and OA.

    Here cm and cm.

    ½ mark

  2. AB is a tangent to the smaller circle at P, so [tangent ⟂ radius].

    Also, the perpendicular from the centre to a chord bisects the chord. So .

    1 mark

  3. In right , by Pythagoras theorem:

    So cm.

    1 mark

  4. cm

    ½ mark

Answer: 8 cm

Where the marks are

  • Correct figure (½ mark)
  • States (tangent ⟂ radius) and hence (1 mark)
  • Uses Pythagoras to get cm (1 mark)
  • Gets cm (½ 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 paper2023 board paper, set 30/4/1 (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.