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Two concentric circles… (Class 10 Maths Basic 2023, Q31B)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 31(B)

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section C, question 31(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31(B) · 3 marks · Short answerCircles

Two concentric circles with centre are of radii cm and cm. Find the length of chord of the larger circle which touches the smaller circle at .

Figure in the paper: Two concentric circles with centre O. The smaller circle has radius 3 cm and the larger circle has radius 5 cm. A chord AB of the larger circle is drawn horizontally, touching the smaller circle at P, which lies at the midpoint of AB directly below O. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

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

Hint 1

AB is a tangent to the smaller circle at P — what is the angle OPA?

Hint 2

Use Pythagoras in △OPA with OA = 5 cm and OP = 3 cm, then double AP.

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. Join OA and OP. AB touches the smaller circle at P, so [radius ⟂ tangent at point of contact].

    ½ mark

  2. AB is a chord of the larger circle and , so [perpendicular from centre bisects the chord].

    1 mark

  3. In right :

    ½ mark

  4. cm

    ½ mark

  5. cm

    ½ mark

Answer: AB = 8 cm

Where the marks are

  • States OP ⟂ AB (½ mark)
  • AP = PB as perpendicular from centre bisects chord (1 mark)
  • Pythagoras: (½ mark)
  • AP = 4 cm (½ mark)
  • AB = 8 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 paper2023 board paper, set 430/4/1 (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.