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A circle touches… (Class 10 Maths Basic SQP 2023-24, Q29)

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MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 29

From the official CBSE sample question paper for 2023-24, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerCircles

A circle touches all the four sides of quadrilateral ABCD. Prove that .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Each vertex of the quadrilateral is an external point from which two tangents are drawn to the circle.

Hint 2

Write the four pairs of equal tangent lengths, add them, and regroup the segments into the sides.

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. Given: A circle touches sides AB, BC, CD and DA of quadrilateral ABCD at P, Q, R and S respectively. To prove: . (Figure: quadrilateral ABCD with the inscribed circle touching AB at P, BC at Q, CD at R and DA at S.)

    1 mark

  2. Tangents drawn from an external point to a circle are equal in length, so:
    ...(1), ...(2), ...(3), ...(4)

    1 mark

  3. Adding (1) to (4):

    . Hence proved.

    1 mark

Answer: proved using equal tangents from external points

Where the marks are

  • Given, to prove and labelled figure (1 mark)
  • Four pairs of equal tangents with reason (1 mark)
  • Adds the equalities and regroups to get the result (1 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 paperSample paper 2023-24 (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.