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PA is a tangent to the circle… (Class 10 Maths 2023, Q24)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 24

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, 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 given figure, PA is a tangent to the circle drawn from the external point P and PBC is the secant to the circle with BC as diameter. If , then find the measure of , where O is the centre of the circle.

Figure in the paper: Circle with centre O and diameter BC horizontal (B left, C right, O the centre). External point P on the left, on the line BC extended. PA is a tangent touching the circle at A (upper left). OA is drawn, and the angle AOC = 130° is 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 30/6/1.

Hints

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

Hint 1

Angles AOB and AOC lie on the straight line BC.

Hint 2

What angle does a tangent make with the radius at the point of contact? Then use triangle OAP.

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. BOC is a straight line, so [linear pair].

    ½ mark

  2. [tangent ⟂ radius at the point of contact].

    ½ mark

  3. In : [angle sum property].

    1 mark

Answer:

Where the marks are

  • Finds (½ mark)
  • Uses (½ mark)
  • Uses the angle sum of to get (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 30/6/1 (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.