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PQ and PR are tangents to a… (Class 10 Maths 2026, Q2)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 2

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section A, question 2, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q2 · 1 mark · MCQCircles

In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If , then the length of each tangent is :

  1. (A) cm
  2. (B)3 cm
  3. (C)6 cm
  4. (D) cm

Figure in the paper: Circle with centre O and radius 3 cm. External point P with two tangents PQ and PR touching the circle at Q and R. Radii OQ and OR are drawn. The angle at P, QPR, is marked 60°. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

Join OP. Which angle does OP make with each tangent?

Hint 2

Triangle OQP has a right angle at Q and an angle of 30° at P. Use tan 30°.

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]. bisects , so .

  2. In right : , so .

  3. Hence cm, which is option (A).

    1 mark

Answer: cm; option (A)

Where the marks are

  • Chooses option (A) cm (1 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 30/3/1 (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.