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TP is tangent to a… (Class 10 Maths Basic 2026, Q24b)

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MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 24(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section B, question 24(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(b) · 2 marks · Very short answerCircles

In the given figure, TP is tangent to a circle with centre O. Diameter BA when produced meets the tangent at T. If , then find the measure of .

Figure in the paper: Circle with centre O; diameter BA extended beyond A to meet tangent TP at T; P is a point on the circle; chords BP and AP are drawn; ∠ABP = 35° is marked at B. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

Join OP; triangle OBP has two equal sides.

Hint 2

Find using the linear pair at O.

Hint 3

The radius OP is perpendicular to the tangent at P; use angle sum in triangle OPT.

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. In , (radii), so . Hence and [linear pair].

    1 mark

  2. [tangent ⟂ radius]. In : , i.e. .

    1 mark

Answer:

Where the marks are

  • Uses to get (or ) (1 mark)
  • Uses and angle sum to get (1 mark)

Revise the chapter

  • Chapter: Circles (notes, formulas, where marks are lost and every past question)
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 430/4/1 (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.