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TP and TQ are two… (Class 10 Maths Basic 2025, Q23)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 23

Set in the CBSE Class 10 board exam of 2025, paper 430/3/1, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerCircles

In the given figure, TP and TQ are two tangents. If , then find the measure of .

Figure in the paper: A circle with centre O; external point T with tangents TP and TQ touching the circle at P and Q. Chord PQ is drawn, and angle PTQ = 50° is marked at T. Angle OPQ is marked at P between PO and PQ. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/3/1.

Hints

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

Hint 1

Triangle TPQ has two equal sides. Why?

Hint 2

Find ∠TPQ first, then use the angle between a radius and a tangent.

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. [tangents drawn from an external point are equal]. So [angles opposite equal sides].

    ½ mark

  2. In : , so .

    1 mark

  3. [tangent ⟂ radius at the point of contact]. So .

    ½ mark

Answer: ∠OPQ = 25°

Where the marks are

  • Uses TP = TQ to get ∠TPQ = ∠TQP (½ mark)
  • Finds ∠TPQ = 65° from the angle sum of the triangle (1 mark)
  • Uses OP ⟂ TP to get ∠OPQ = 25° (½ 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 430/3/1 (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.