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TP and TQ are two… (Class 10 Maths Basic 2026, Q23)

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MathsCBSE Class 10 · Basic · Board exam 2026, set 430/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 23

Set in the CBSE Class 10 board exam of 2026, 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: Circle with centre O, external point T with tangents TP and TQ touching the circle at P and Q. Chord PQ is drawn; angle PTQ = 50° is marked at T; angle OPQ is marked at P. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/3/1.

Hints

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

Hint 1

Tangents drawn from T are equal, so is isosceles.

Hint 2

The radius OP makes a right angle with the tangent TP.

Hint 3

Subtract from .

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 from an external point are equal], so in : .

    1 mark

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

    ½ mark

  3. .

    ½ mark

Answer:

Where the marks are

  • Uses equal tangents to find (1 mark)
  • States with reason (½ mark)
  • Obtains (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 paper2026 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.