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If tangents PA and PB drawn from… (Class 10 Maths 2025, Q8)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 8

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, section A, question 8, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q8 · 1 mark · MCQCircles

If tangents PA and PB drawn from an external point P to the circle with centre O are inclined to each other at an angle of as shown in the given figure, then the measure of POA is :

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

Figure in the paper: A circle with centre O. External point P on the left. Two tangents from P touch the circle at A (upper) and B (lower). The angle APB is marked at P. The line PO is drawn horizontally from P through to O. OA and OB are radii. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

The line from P to the centre bisects the angle between tangents.

Hint 2

Radius is perpendicular to tangent; use angle sum in 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. PO bisects , so ; [tangent ⟂ radius].

    ½ mark

  2. In : . Option (B).

    ½ mark

Answer: , option (B)

Where the marks are

  • Uses and (½ mark)
  • Angle sum gives (½ 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 30/3/1 (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.