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PA is a tangent from an… (Class 10 Maths 2026, Q13)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 13

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section A, question 13, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q13 · 1 mark · MCQCircles

In the given figure, PA is a tangent from an external point P to a circle with centre O. If , then is equal to :

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

Figure in the paper: A circle with centre O. P is an external point on the left. PA is a tangent touching the circle at A (top). A straight line passes through A, O and continues to B on the lower right of the circle, so AB is a diameter. The line PO is drawn from P to O. The angle POB = 125° is marked at O between OP and OB. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

Hints

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

Hint 1

∠AOP and ∠POB form a linear pair.

Hint 2

The radius OA is perpendicular to the tangent PA.

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. AOB is a straight line, so .

  2. [tangent ⟂ radius]. In : . Option (d).

    1 mark

Answer: , option (d)

Where the marks are

  • Finds ∠AOP = 55°, uses ∠OAP = 90° and gets 35°, option (d) (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 paper2026 board paper, set 30/1/1 (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.