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A circle with centre O and… (Class 10 Maths 2024, Q30B)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 30(B)

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section C, question 30(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(B) · 3 marks · Short answerCircles

A circle with centre O and radius 8 cm is inscribed in a quadrilateral ABCD in which P, Q, R, S are the points of contact as shown. If AD is perpendicular to DC, BC = 30 cm and BS = 24 cm, then find the length DC.

Figure in the paper: Quadrilateral ABCD with the circle inscribed. A top-left, B top-right, C bottom-right, D bottom-left with a right angle at D. S is the touching point on side AB, P on side AD, Q on side DC, R on side BC. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

Hints

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

Hint 1

Tangents drawn from the same external point are equal. Start with BR.

Hint 2

Join OP and OQ. With the right angle at D, what kind of quadrilateral is OPDQ?

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 OP and OQ.

    cm [tangents from the external point B are equal].

    ½ mark

  2. cm.

    ½ mark

  3. cm [tangents from C are equal].

    ½ mark

  4. In quadrilateral OPDQ: and [tangent ⟂ radius]. Also OP = OQ = 8 cm, so OPDQ is a square.

    cm.

    ½ mark

  5. cm.

    1 mark

Answer: DC = 14 cm

Where the marks are

  • cm (½ mark)
  • cm (½ mark)
  • cm (½ mark)
  • cm, since OPDQ is a square (½ mark)
  • cm (1 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 30/1/1 (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.