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PQ is a tangent to the circle… (Class 10 Maths 2023, Q14)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 14

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section A, question 14, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q14 · 1 mark · MCQCircles

In the given figure, PQ is a tangent to the circle with centre O. If , , then is:

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

Figure in the paper: A circle with centre O. A tangent line passes through Q on the circle and the point P outside the circle, so PQ is the tangent. P, O are on a horizontal line; the segment PO joins P to the centre O. Angle at P between PQ and PO is marked x, and angle at O between OP and OQ is marked y. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/4/1.

Hints

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

Hint 1

What is the angle between a tangent and the radius at the point of contact?

Hint 2

Apply the angle sum property to triangle OPQ.

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 at the point of contact].

  2. In : [angle sum property].

  3. . So the answer is option (B).

    1 mark

Answer: , option (B)

Where the marks are

  • Chooses option (B) (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 paper2023 board paper, set 30/4/1 (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.