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Two concentric circles are of… (Class 10 Maths 2026, Q25)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 25

Set in the CBSE Class 10 board exam of 2026, 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

Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.

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

Hints

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

Hint 1

The chord is a tangent to the smaller circle. What angle does it make with the radius at the point of contact?

Hint 2

Form a right triangle with OA = 5 cm as hypotenuse and OM = 4 cm as one side.

Hint 3

The perpendicular from the centre bisects the chord, so double the half-length.

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. Figure: Two circles with common centre O. Inner radius 4 cm, outer radius 5 cm. Chord AB of the larger circle touches the smaller circle at M. Join OA and OM.

    ½ mark

  2. OM is the radius of the smaller circle and AB is a tangent to it at M, so [tangent ⟂ radius]. Also OM = 4 cm and OA = 5 cm.

    In right : cm.

    1 mark

  3. The perpendicular from the centre to a chord bisects the chord, so M is the mid-point of AB.

    cm.

    ½ mark

Answer: Length of chord = 6 cm

Where the marks are

  • Draws a correct labelled figure (½ mark)
  • Uses OM ⟂ AB and Pythagoras to get AM = 3 cm (1 mark)
  • Uses the perpendicular bisecting the chord to get AB = 6 cm (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 paper2026 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.