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O is the centre of the circle… (Class 10 Maths 2023, Q25)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 25

Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerCircles

In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If , then find the measure of .

Figure in the paper: A circle with centre O. External point A on the left with two tangents AB and AC touching the circle at B (upper) and C (lower). Radii OB and OC are drawn. Angle BAC = 65° is marked at A. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.

Hints

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

Hint 1

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

Hint 2

Use the angle sum of quadrilateral ABOC.

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].
    The angles of quadrilateral ABOC add up to , so .

    1 mark

  2. 1 mark

Answer:

Where the marks are

  • Uses , with the reason tangent ⟂ radius (1 mark)
  • Gets (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 30/2/1 (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.