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TP and TQ are tangents at… (Class 10 Maths Basic 2026, Q29)

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

CBSE Class 10 Mathematics Basic 2026: question 29

Set in the CBSE Class 10 board exam of 2026, paper 430/2/1, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerCircles

In the given figure, TP and TQ are tangents at points P and Q of the circle respectively. If reflex , find the measure of each angle of quadrilateral POQT.

Figure in the paper: Circle with centre O. Points P and Q on the circle; T is outside the circle with tangents TP and TQ. The quadrilateral POQT is formed by OP, PT, TQ and QO. The reflex angle POQ is marked as at O. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/2/1.

Hints

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

Hint 1

The reflex angle and the ordinary angle at O together make .

Hint 2

What angle does a tangent make with the radius at the point of contact?

Hint 3

Use the fact that the angles of a quadrilateral add up to .

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. (inside the quadrilateral) .

    1 mark

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

    1 mark

  3. The angle sum of quadrilateral POQT is , so .

    1 mark

Answer: ∠POQ = 110°, ∠OPT = 90°, ∠OQT = 90°, ∠PTQ = 70°

Where the marks are

  • Finds (1 mark)
  • States with the reason (1 mark)
  • Finds (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 430/2/1 (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.