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O is the centre of the circle… (Class 10 Maths 2025, Q26a)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 26(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, section C, question 26(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26(a) · 3 marks · Short answerCircles

In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that .

Figure in the paper: Circle with centre O. Line BCD is tangent at C (B left, D right). Line from B passes through P (on circle) and O to A on the circle. OC (dashed) and AC are joined. Angle BAC is marked at A. 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

OA and OC are both radii. What does that tell you about ?

Hint 2

Radius OC meets the tangent BD at . Split into two parts and substitute.

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. In , (radii of the same circle). Therefore [angles opposite equal sides].

    1 mark

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

    1 mark

  3. , so .

    ½ mark

  4. Using : . Since O lies on AB, . Hence . Proved.

    ½ mark

Answer: (proved)

Where the marks are

  • Uses OA = OC to get (1 mark)
  • States (tangent ⟂ radius) (1 mark)
  • Writes (½ mark)
  • Substitutes to conclude (½ 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 30/1/1 (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.