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PA and PB are tangents to a… (Class 10 Maths 2025, Q9)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 9

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section A, question 9, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q9 · 1 mark · MCQCircles

In the adjoining figure, PA and PB are tangents to a circle with centre O such that . If cm, then the diameter of the circle is

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

Figure in the paper: A circle with centre O. Two tangents meet at external point P, touching the circle at A (bottom) and B (right). OA and OB are radii, OA is vertical, OB horizontal, forming a square OAPB with a right angle at P. The chord AB is drawn as a diagonal inside the square. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

What angle does a radius make with a tangent?

Hint 2

AB is the diagonal of a square of side r.

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 OAPB is a square with diagonal AB.

    ½ mark

  2. Side cm = radius, so diameter = 6 cm. Option (D).

    ½ mark

Answer: 6 cm, option (D)

Where the marks are

  • Recognises OAPB as a square (½ mark)
  • Radius 3 cm, diameter 6 cm (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 paper2025 board paper, set 30/6/1 (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.