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Prove that a parallelogram… (Class 10 Maths Basic 2026, Q26)

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MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2026: question 26

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerCircles

Prove that a parallelogram circumscribing a circle, is a rhombus.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

Mark the points where the circle touches each side.

Hint 2

From each vertex, two tangents are drawn to the circle; they are equal.

Hint 3

Add all four equalities and 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: parallelogram ABCD with a circle inside touching AB at P, BC at Q, CD at R and DA at S. Given: ABCD is a parallelogram circumscribing the circle. To prove: ABCD is a rhombus.

    ½ mark

  2. Tangents from an external point are equal: , , , .

    1 mark

  3. Adding: , i.e. , so .

    1 mark

  4. In a parallelogram and , so . Adjacent sides are equal, so all four sides are equal; hence ABCD is a rhombus.

    ½ mark

Answer: AB = BC = CD = DA, so ABCD is a rhombus.

Where the marks are

  • Correct labelled figure (½ mark)
  • Writes the four pairs of equal tangents (1 mark)
  • Adds to get (1 mark)
  • Uses opposite sides equal to conclude , rhombus (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 paper2026 board paper, set 430/4/1 (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.