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Prove that the… (Class 10 Maths SQP 2026-27, Q29)

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MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 29

From the official CBSE sample question paper for 2026-27, 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

Prove that the parallelogram circumscribing a circle is a rhombus.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

Mark the four points of contact. From each vertex, two tangents are drawn to the circle; what do you know about their lengths?

Hint 2

Add the equal tangent lengths to get , then use the fact that opposite sides of a parallelogram are equal.

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: ABCD is a parallelogram whose sides AB, BC, CD and DA touch a circle with centre O at S, P, Q and R respectively.

    Tangents drawn from an external point to a circle are equal in length, so:

    …(i)

    …(ii)

    …(iii)

    …(iv)

    1 mark

  2. Adding (i), (ii), (iii) and (iv):

    .

    1 mark

  3. In a parallelogram, opposite sides are equal, so and .

    .

    So the adjacent sides of parallelogram ABCD are equal, and all four sides are equal. Hence ABCD is a rhombus.

    1 mark

Answer: Proved: , so the parallelogram ABCD is a rhombus.

Where the marks are

  • Writes the four pairs of equal tangent lengths with the reason (1 mark)
  • Adds them to get (1 mark)
  • Uses opposite sides of a parallelogram being equal to get and concludes it is a rhombus (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 2026-27 (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.