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Prove that the lengths… (Class 10 Maths Basic 2024, Q29b)

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MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2024: question 29(b)

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, 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

Prove that the lengths of the 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 2024 board paper, set 430/5/1.

Hints

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

Hint 1

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

Hint 2

The angle between a tangent and the radius at the point of contact is 90°; look for congruent right triangles.

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: a circle with centre O, an external point P, and tangents PA and PB touching the circle at A and B.
    Given: PA and PB are tangents from P. To prove: .

    ½ mark

  2. Construction: Join OA, OB and OP.

    ½ mark

  3. In and : [radii], [common], [tangent ⟂ radius at point of contact]

    1 mark

  4. [RHS congruence]

    ½ mark

  5. [CPCT]. Hence proved.

    ½ mark

Answer: PA = PB, proved by RHS congruence.

Where the marks are

  • Correct figure with given/to prove (½ mark)
  • Construction: join OA, OB, OP (½ mark)
  • Lists equal parts with right angles from tangent ⟂ radius (1 mark)
  • States RHS congruence (½ mark)
  • Concludes PA = PB by CPCT (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 paper2024 board paper, set 430/5/1 (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.