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PT is a tangent to the circle… (Class 10 Maths 2026, Q12)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 12

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section A, question 12, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q12 · 1 mark · MCQCircles

In the given figure, PT is a tangent to the circle with centre O and radius r. If , then the length of OP is :

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

Figure in the paper: Circle with centre O and radius r. Point T on the circle with tangent PT at T; P is an external point, OP is drawn, and the angle POT is marked 45°. OT is labelled r. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

Triangle OTP is right-angled. Where is the right angle?

Hint 2

OT is adjacent to the 45° angle and OP is the hypotenuse.

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. , which is option (A).

    1 mark

Answer: ; option (A)

Where the marks are

  • Chooses option (A) (1 mark)

Revise the chapter

  • Chapter: Circles (notes, formulas, where marks are lost and every past question)
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 30/3/1 (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.