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AB and CD are tangents to a… (Class 10 Maths 2024, Q24)

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

CBSE Class 10 Mathematics Standard 2024: question 24

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerCircles

In the given figure, and are tangents to a circle centred at . Is ? Justify your answer.

Figure in the paper: Circle with centre O. Two tangent lines touch the circle at A (lower-left) and C (lower-right). Line AB extends from A up-left to point B, and line CD extends from C up-right to point D. Chord AC is drawn horizontally between the two points of contact. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 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 two points of contact.

Hint 2

Triangle OAC is isosceles; and what angle does a tangent make with the radius?

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. Yes. Join and . [radii of the same circle].

    ½ mark

  2. In , [angles opposite equal sides].

    ½ mark

  3. [tangent ⟂ radius at point of contact]. Adding: .

    ½ mark

  4. . Hence the two angles are equal.

    ½ mark

Answer: Yes, .

Where the marks are

  • Joins OA, OC and uses OA = OC (½ mark)
  • (½ mark)
  • Uses and adds angles (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 30/2/1 (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.