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If O is centre of a… (Class 10 Maths SQP 2023-24, Q9)

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MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 9

From the official CBSE sample question paper for 2023-24, section A, question 9, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q9 · 1 mark · MCQCircles

If O is centre of a circle and Chord PQ makes an angle with the tangent PR at the point of contact P, then the angle subtended by the chord at the centre is

  1. (A)
  2. (B)
  3. (C)
  4. (D)

Figure in the paper: Circle with centre O. Chord PQ, with P on the circle. Tangent PR touches the circle at P, extending to the right. O is joined to P and to Q, forming triangle OPQ. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

The radius OP is perpendicular to the tangent PR.

Hint 2

Triangle OPQ is isosceles.

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. [tangent ⟂ radius]. So .

  2. (radii), so .

  3. . Option (B).

    1 mark

Answer: , option (B)

Where the marks are

  • Uses tangent ⟂ radius and the isosceles triangle OPQ to get , option (B) (1 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 paperSample paper 2023-24 (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.