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Tangents PA and PB drawn… (Class 10 Maths Basic 2024, Q1)

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MathsCBSE Class 10 · Basic · Board exam 2024, set 430/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2024: question 1

Set in the CBSE Class 10 board exam of 2024, paper 430/3/1, section A, question 1, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q1 · 1 mark · MCQCircles

In the given figure, tangents and drawn from to circle are inclined to each other at an angle of . The measure of is

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

Figure in the paper: A circle with centre O. An external point P has two tangents touching the circle at A and B. The chord AB is drawn. The angle at P between the two tangents is marked . The angle is to be found. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/3/1.

Hints

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

Hint 1

Compare the lengths PA and PB.

Hint 2

Triangle PAB is isosceles; use the angle sum property.

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. [tangents from an external point are equal], so is isosceles and .

  2. , option (C).

    1 mark

Answer: , option (C)

Where the marks are

  • Uses and the angle sum 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 paper2024 board paper, set 430/3/1 (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.