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PQ is tangent to a circle with… (Class 10 Maths 2026, Q14)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 14

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section A, question 14, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q14 · 1 mark · MCQCircles

PQ is tangent to a circle with centre O. If , then is

  1. (A)65°
  2. (B)58.5°
  3. (C)57.5°
  4. (D)45°

Figure in the paper: Circle with centre O; tangent line PQ touches circle at P; S is diametrically opposite P (SP is a diameter); R is a point on the circle; angle POR = 65°; line SR extended meets the tangent at T (T lies between P and Q); angle PTR is marked. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

Arc PR subtends 65° at O; what does it subtend at S?

Hint 2

Use the right angle between tangent and diameter at P.

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. [angle at centre is twice angle at circumference]. [tangent ⟂ radius].

  2. In : .

    1 mark

Answer: 57.5°, option (C)

Where the marks are

  • Gets and angle sum gives 57.5° (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 30/4/1 (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.