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O is the centre of the circle… (Class 10 Maths 2026, Q25)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 25

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerCircles

In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.

Figure in the paper: Circle with centre O. P is outside the circle on the left. PR is a tangent touching the circle at R (upper left); PQ is a tangent touching the circle at Q (bottom). Radii OR and OQ are drawn; OQ is vertical and OR is drawn to the tangent point R. Ray from P through R and horizontal ray from P through Q are shown with arrowheads. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

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

Hint 1

What angle does a radius make with the tangent at the point of contact?

Hint 2

A quadrilateral is cyclic if a pair of opposite angles adds up to 180°.

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. The tangent at any point of a circle is perpendicular to the radius through the point of contact, so and

    1 mark

  2. ½ mark

  3. In quadrilateral PQOR, one pair of opposite angles is supplementary (then the other pair also sums to ), so PQOR is cyclic.

    ½ mark

Answer: , hence PQOR is cyclic.

Where the marks are

  • States with reason tangent ⟂ radius (1 mark)
  • Adds to get (½ mark)
  • Concludes cyclic since opposite angles are supplementary (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 paper2026 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.