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If PQ and PR are tangents to the… (Class 10 Maths 2026, Q4)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 4

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section A, question 4, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q4 · 1 mark · MCQCircles

If PQ and PR are tangents to the circle with centre O and radius 4 cm such that , then the length OP is

  1. (A)4 cm
  2. (B) cm
  3. (C)8 cm
  4. (D) cm

Figure in the paper: Circle with centre O; external point P; tangents PQ and PR touch the circle at Q and R; OQ, OR and OP are joined; angle QPR = 90°. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

Radius to point of contact is perpendicular to the tangent.

Hint 2

All four angles of OQPR are right angles.

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. [tangent ⟂ radius] and , with , so OQPR is a square of side 4 cm.

  2. OP is its diagonal: cm.

    1 mark

Answer: cm, option (B)

Where the marks are

  • Recognises square OQPR and gets cm (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 paper2026 board paper, set 30/4/1 (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.