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PA is a tangent… (Class 10 Maths Basic SQP 2025-26, Q16)

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MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 16

From the official CBSE sample question paper for 2025-26, section A, question 16, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q16 · 1 mark · MCQCircles

In the given figure, PA is a tangent from an external point P to a circle with centre O and diameter AB. If , then measure of is

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

Figure in the paper: A circle with centre O and diameter AB (A at top-left, B at bottom-right). External point P lies to the lower-left; PA is a tangent touching the circle at A. Segment PO is drawn to the centre; the angle POB at O is marked as 115°. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

What is the angle between a tangent and the radius at the point of contact?

Hint 2

is an exterior angle of .

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. [tangent ⟂ radius].

  2. is an exterior angle of , so , option (A).

    1 mark

Answer: 25°, option (A)

Where the marks are

  • Uses the right angle and the exterior angle property to get 25° (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 paperSample paper 2025-26 (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.