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PT is a tangent at T to… (Class 10 Maths Basic 2023, Q24)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 24

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerCircles

In the adjoining figure, PT is a tangent at T to the circle with centre O. If , find the value of .

Figure in the paper: A circle with centre O. P is a point outside the circle, and PT is a tangent touching the circle at T. OT is a radius and OP is joined. The angle TPO = 30° is marked at P. The angle x is marked at the centre O, below the line OP. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

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

Find using the angle sum of , then use the straight line through T and O.

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]

    1 mark

  2. In : . Since TO produced is a straight line, [linear pair]

    1 mark

Answer: x = 120°

Where the marks are

  • Uses (tangent ⟂ radius) (1 mark)
  • Finds and by linear pair (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 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.