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PA is a tangent from an… (Class 10 Maths 2025, Q16)

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

CBSE Class 10 Mathematics Standard 2025: question 16

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, 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. If , then is equal to :

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

Figure in the paper: Circle with centre O. AB is a diameter through O (A at top, B at bottom right). PA is a tangent at A from external point P on the left. PO is drawn to O. Angle POB is marked 115°. See it in the official paper.

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

Hints

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

Hint 1

AB is a straight line. What is ?

Hint 2

The tangent at A is perpendicular to OA. Now use the angle sum 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. AOB is a straight line (a diameter), so [linear pair].

  2. [tangent ⟂ radius at the point of contact].

  3. In : , so the answer is option (A).

    1 mark

Answer: , option (A)

Where the marks are

  • Chooses option (A) (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 30/1/1 (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.