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O is the centre of a… (Class 10 Maths Basic 2023, Q2)

questionbuddy.in/q/cbse-10-maths-2023-430-5-1-q2-centre-circle-chord-tangent-makes

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2023: question 2

Set in the CBSE Class 10 board exam of 2023, paper 430/5/1, section A, question 2, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q2 · 1 mark · MCQCircles

In the given figure, O is the centre of a circle, PQ is a chord and the tangent PT at P makes an angle of with PQ. The measure of is:

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

Figure in the paper: A circle with centre O. A chord PQ is drawn. A tangent PT is drawn at point P, extending to the right. The angle between the tangent PT and chord PQ is marked . OP and OQ are radii joining the centre O to P and Q. The angle POQ is at the centre. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/5/1.

Hints

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

Hint 1

What angle does a radius make with the tangent at its point of contact?

Hint 2

Triangle OPQ is isosceles since OP = OQ.

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 . Since OP = OQ, .

  2. , option (B)

    1 mark

Answer: 100°, option (B)

Where the marks are

  • Correct option (B) 100° (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 paper2023 board paper, set 430/5/1 (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.