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If O is the centre of a… (Class 10 Maths Basic 2024, Q27b)

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MathsCBSE Class 10 · Basic · Board exam 2024, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2024: question 27(b)

Set in the CBSE Class 10 board exam of 2024, paper 430/4/1, section C, question 27(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(b) · 3 marks · Short answerCircles

If O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of with PQ, then find the measure of .

Figure in the paper: Circle with centre O. Chord PQ drawn with P on the circle at the top and Q on the right side of the circle. Radii OP and OQ are drawn. At P, a tangent line PR extends horizontally to the right with an arrow; the angle between tangent PR and chord PQ is marked 40°. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/4/1.

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

Find ∠OPQ first. Triangle OPQ is isosceles, so then use its angle sum.

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. [radius ⟂ tangent at the point of contact], and (given). So .

    1 mark

  2. In , [radii], so [angles opposite equal sides].

    1 mark

  3. By the angle sum property, .

    1 mark

Answer: ∠POQ = 80°

Where the marks are

  • ∠OPQ = 50° using radius ⟂ tangent (1 mark)
  • ∠OQP = 50° because OP = OQ (1 mark)
  • ∠POQ = 80° by angle sum (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 paper2024 board paper, set 430/4/1 (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.