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AC and AB are tangents to a… (Class 10 Maths 2023, Q16)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 16

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, section A, question 16, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q16 · 1 mark · MCQCircles

In the given figure, AC and AB are tangents to a circle centred at O. If , then is equal to :

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

Figure in the paper: A circle with centre O and diameter AD passing through the line from external point A. AB and AC are tangents touching the circle at B and C. Angle COD = 120° marked at O. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/5/1.

Hints

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

Hint 1

A, O, D lie on a line; find ∠AOC.

Hint 2

Use the right angle at C and symmetry of tangents.

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. (linear pair), [tangent ⟂ radius], so .

  2. (OA bisects angle between tangents). Option (A).

    1 mark

Answer: 30°, option (A)

Where the marks are

  • Finds ∠AOC = 60° and ∠BAO = 30° (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 30/5/1 (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.