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If two tangents inclined at an… (Class 10 Maths 2024, Q21a)

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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(a)

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

Q21(a) · 2 marks · Very short answerCircles

If two tangents inclined at an angle of are drawn to a circle of radius 3 cm, then find the length of each tangent.

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

Join the centre to the point of contact and to the external point. What angle does the radius make with the tangent?

Hint 2

The line from the external point to the centre bisects the 60° angle between the tangents.

Hint 3

In the right triangle you now have, the radius is opposite the 30° angle; use tan 30°.

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: Draw a circle with centre O and radius OA = OB = 3 cm. From an external point P draw tangents PA and PB with . Join OA, OB and OP.

    ½ mark

  2. [tangent ⟂ radius]. OP bisects [tangents from an external point are equally inclined to OP], so .

    ½ mark

  3. In right :

    ½ mark

  4. cm. Since tangents from an external point are equal, cm.

    ½ mark

Answer: Each tangent = cm

Where the marks are

  • Correct labelled figure (½ mark)
  • States (½ mark)
  • Writes (½ mark)
  • Gets cm (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 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.