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Prove that the tangents drawn… (Class 10 Maths 2024, Q21b)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 21(b)

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, section B, question 21(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(b) · 2 marks · Very short answerCircles

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

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

Hint 1

Draw the diameter AB and the tangents at A and B.

Hint 2

What angle does each tangent make with the diameter?

Hint 3

Treat the diameter as a transversal and use the co-interior angles property.

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 and diameter AB. Line PQ is the tangent at A (P and Q on either side of A), and line RS is the tangent at B (R above P, S above Q).

    ½ mark

  2. and [tangent ⟂ radius at the point of contact]

    ½ mark

  3. . These are co-interior angles made by the transversal AB with the lines PQ and RS, and they are supplementary.

    ½ mark

  4. Therefore , i.e. the tangents at the ends of a diameter are parallel.

    ½ mark

Answer: The co-interior angles at A and B add to , so the tangents PQ and RS are parallel.

Where the marks are

  • Correct figure (½ mark)
  • Both angles with reason (½ mark)
  • Sum , co-interior angles supplementary (½ mark)
  • Concludes (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 30/5/1 (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.