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Find the radius of… (Class 10 Maths Basic SQP 2025-26, Q22)

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MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 22

From the official CBSE sample question paper for 2025-26, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerCircles

Find the radius of the circle with centre at origin, if line given by is tangent to the circle at point P.

Figure in the paper: A circle with centre C(0, 0). A horizontal line touches the circle at the point P(3, a) at the bottom of the circle; a dashed radius joins C to P. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

The point of contact P lies on the tangent line, so its coordinates satisfy .

Hint 2

Once you know P, the radius is the distance from the centre (0, 0) to P.

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. P(3, a) lies on the line , so . Hence P is (3, 2).

    1 mark

  2. Radius = CP units.

    1 mark

Answer: Radius = units

Where the marks are

  • Substitutes P in the line to get (1 mark)
  • Uses distance formula to get radius units (1 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 paperSample paper 2025-26 (Basic): 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.