Skip to content

A person is standing at P… (Class 10 Maths 2025, Q25)

questionbuddy.in/q/cbse-10-maths-2025-30-1-1-q25-person-standing-outside-circular-ground

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 25

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, 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

A person is standing at P outside a circular ground at a distance of 26 m from the centre of the ground. He found that his distances from the points A and B on the ground are 10 m (PA and PB are tangents to the circle). Find the radius of the circular ground.

Figure in the paper: Circle with centre O. External point P on the left, PO = 26 m drawn. Tangents PA and PB (each 10 m) touch the circle at A (top) and B (bottom). OA and OB are joined. See it in the official paper.

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

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

Use Pythagoras theorem in with OP as the hypotenuse.

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 at the point of contact].

    ½ mark

  2. In right , by Pythagoras theorem:

    1 mark

  3. . Radius of the ground m.

    ½ mark

Answer: Radius = 24 m

Where the marks are

  • States (½ mark)
  • Applies Pythagoras: (1 mark)
  • Radius = 24 m (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 paper2025 board paper, set 30/1/1 (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.