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If a circle touches the side… (Class 10 Maths 2026, Q29B)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 29(B)

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section C, question 29(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(B) · 3 marks · Short answerCircles

In the given figure, if a circle touches the side QR of PQR at S and extended sides PQ and PR at M and N respectively, then prove that :

Figure in the paper: Triangle PQR with apex P at top, Q bottom-left, R bottom-right. A circle lies below side QR, touching QR at S, and touching the extended sides PQ (at M, on the lower left extension) and PR (at N, on the lower right extension). See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

Hints

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

Hint 1

Look for pairs of tangents drawn from the same point (P, Q and R).

Hint 2

Write PM as PQ + QM and PN as PR + RN, then add.

Hint 3

Replace QM and RN by the equal tangent lengths on QR.

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. Tangents drawn from an external point to a circle are equal in length. So:

    • from P:
    • from Q:
    • from R:
    1½ marks

  2. Since M lies on PQ extended and N lies on PR extended, and . Adding:

    ½ mark

  3. Using , and :

    ½ mark

  4. Since S lies on QR, . So

    Hence proved.

    ½ mark

Answer: (proved)

Where the marks are

  • States the three pairs of equal tangents PM = PN, QS = QM, RS = RN (1½ marks)
  • Writes PM + PN = PQ + QM + PR + RN (½ mark)
  • Substitutes to get 2PM = PQ + QS + RS + PR (½ mark)
  • Uses QS + SR = QR to conclude the result (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 paper2026 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.