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TP and TQ are tangents at… (Class 10 Maths Basic 2025, Q29)

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

CBSE Class 10 Mathematics Basic 2025: question 29

Set in the CBSE Class 10 board exam of 2025, 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 POQ = , find the measure of each angle of quadrilateral POQT.

Figure in the paper: A circle with centre O. T is outside the circle, with tangent segments TP and TQ touching the circle at P (upper left) and Q (right). Radii OP and OQ are drawn. The reflex angle POQ, marked 250 degrees, is shown at O on the inside of the major arc. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/2/1.

Hints

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

Hint 1

The reflex angle and the angle POQ inside the quadrilateral together make 360°.

Hint 2

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

Hint 3

Angles of a quadrilateral add to 360°.

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. .

    1 mark

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

    1 mark

  3. In quadrilateral POQT, .

    1 mark

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

Where the marks are

  • Finds ∠POQ = 110° (1 mark)
  • ∠OPT = ∠OQT = 90° with reason (1 mark)
  • Uses angle sum of quadrilateral to get ∠PTQ = 70° (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 paper2025 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.