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Prove that the lengths of… (Class 10 Maths 2026, Q29a)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 3 marks · Short answer

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

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section C, question 29(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(a) · 3 marks · Short answerCircles

Prove that the lengths of tangents drawn from an external point to a circle are equal.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

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

Hint 1

Join the centre to the external point and to both points of contact.

Hint 2

The angle between tangent and radius is 90°; look for RHS congruence.

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: circle with centre O; from external point P draw tangents PQ and PR touching the circle at Q and R; join OP, OQ, OR.

    1 mark

  2. Given: PQ and PR are tangents from external point P to a circle with centre O. To prove: . Construction: join OP, OQ, OR.

    ½ mark

  3. In and : [radii]; [common]; [tangent ⟂ radius at point of contact]. So [RHS congruence].

    1 mark

  4. Hence [CPCT].

    ½ mark

Answer: PQ = PR (proved)

Where the marks are

  • Correct labelled figure (1 mark)
  • Given, To prove, Construction (½ mark)
  • Proves △OQP ≅ △ORP by RHS with reasons (1 mark)
  • Concludes PQ = PR by CPCT (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 paper2026 board paper, set 30/2/1 (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.