Skip to content

At point A on the diameter AB… (Class 10 Maths 2025, Q25)

questionbuddy.in/q/cbse-10-maths-2025-30-2-1-q25-point-diameter-circle-radius-tangent

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

CBSE Class 10 Mathematics Standard 2025: question 25

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, 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

At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the length of the chord CD parallel to XY at a distance of 16 cm from A.

Figure in the paper: A circle with centre O and horizontal diameter BA (B on left, A on right); OA is marked 10 cm. Vertical tangent line XAY passes through A (X above, Y below). A vertical chord CD is drawn to the left of O, meeting diameter AB at point P; C is on the upper arc and D on the lower arc; OC and OD 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 30/2/1.

Hints

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

Hint 1

Find how far the chord is from the centre O.

Hint 2

The tangent at A is perpendicular to OA, so a chord parallel to it is perpendicular to the diameter.

Hint 3

Use Pythagoras in triangle OPC, then remember that P is the midpoint of CD.

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. Chord CD meets diameter AB at P, and cm.

    cm (radius), so cm.

    ½ mark

  2. [tangent ⟂ radius at the point of contact]. Since , also , so .

    In right , cm (radius):

    1 mark

  3. The perpendicular from the centre bisects the chord, so cm.

    ½ mark

Answer: CD = 16 cm

Where the marks are

  • Finds cm (1/2 mark)
  • Uses and Pythagoras to get cm (1 mark)
  • Doubles to get cm, as the perpendicular from the centre bisects the chord (1/2 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 30/2/1 (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.