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Prove that the tangents… (Class 10 Maths Basic 2023, Q28)

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

CBSE Class 10 Mathematics Basic 2023: question 28

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerCircles

Prove that the tangents drawn from an external point to a circle are equal in length.

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

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 radius is perpendicular to the tangent at the point of contact — 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; from an external point P, tangents PQ and PR touch the circle at Q and R; OP, OQ, OR are joined.

    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].

    1 mark

  4. Hence [CPCT].

    ½ mark

Answer: PQ = PR (tangents from an external point are equal)

Where the marks are

  • Correct figure (1 mark)
  • Given, to prove, construction (½ mark)
  • Proves triangles congruent 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 paper2023 board paper, set 430/1/1 (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.