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There is a circular park of… (Class 10 Maths 2025, Q32a)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 32(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section D, question 32(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(a) · 5 marks · Long answerCompetency-basedCircles

There is a circular park of diameter 65 m as shown in the following figure, where AB is a diameter. An entry gate is to be constructed at a point P on the boundary of the park such that distance of P from A is 35 m more than the distance of P from B. Find distance of point P from A and B respectively.

Figure in the paper: A circle with centre O. AB is a horizontal diameter with A on the left and B on the right. P is a point on the upper arc, joined to A and B forming triangle APB with a right angle at P. 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 is the angle at P, since AB is a diameter?

Hint 2

Use Pythagoras in triangle APB with PB = and PA = , AB = 65.

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. Let m; then m.

    ½ mark

  2. [angle in a semicircle], so by Pythagoras theorem:

    1 mark

  3. 2 marks

  4. ½ mark

  5. (rejecting as distance cannot be negative)

    ½ mark

  6. m and m.

    ½ mark

Answer: Distance from A = 60 m, from B = 25 m

Where the marks are

  • Takes , (½ mark)
  • Applies Pythagoras in right (1 mark)
  • Forms (2 marks)
  • Factorises (½ mark)
  • (½ mark)
  • Distances 60 m and 25 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 30/6/1 (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.