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PA and PB are tangents to a… (Class 10 Maths 2025, Q11)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 11

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section A, question 11, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q11 · 1 mark · MCQCircles

In the adjoining figure, PA and PB are tangents to a circle with centre O. The measure of angle APB is

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

Figure in the paper: A circle with centre O. External point P with two tangents touching the circle at A and B. The reflex angle AOB at the centre, measured through the major arc side, is marked . See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

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

Hint 1

Convert the reflex angle to the angle inside quadrilateral OAPB.

Hint 2

∠APB and ∠AOB are supplementary.

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. Non-reflex .

  2. In quadrilateral OAPB, [tangent ⟂ radius], so . Option (D).

    1 mark

Answer: 30°, option (D)

Where the marks are

  • Finds ∠AOB = 150° and ∠APB = 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 paper2025 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.