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AT is tangent to a circle… (Class 10 Maths 2024, Q17)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 17

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section A, question 17, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q17 · 1 mark · MCQCircles

In the given figure, is tangent to a circle centred at . If , then is equal to

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

Figure in the paper: Circle with centre O. AB is a diameter drawn vertically, with B at the top and A at the bottom of the circle. The line AT is a tangent at A, extending horizontally to the right through T. C is a point on the circle; chord AC and chord BC are drawn. The angle between AC and tangent AT, at A, is marked as 40 degrees. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

AB is a diameter, so ∠ACB = ?

Hint 2

Angle between tangent and radius is 90°.

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 ; [angle in semicircle].

  2. . Option (D).

    1 mark

Answer: 40°, option (D)

Where the marks are

  • Uses tangent ⟂ radius and semicircle angle to get 40° (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 paper2024 board paper, set 30/2/1 (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.