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Prove that the angle… (Class 10 Maths Basic 2025, Q24a)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 24(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/4/1, section B, question 24(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(a) · 2 marks · Very short answerCircles

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/4/1.

Hints

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

Hint 1

Join the centre to both points of contact.

Hint 2

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

Hint 3

Use the angle sum of the quadrilateral OAPB.

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. Figure: a circle with centre O. PA and PB are tangents from the external point P, touching the circle at A and B. Join OA and OB.

    ½ mark

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

    ½ mark

  3. In quadrilateral OAPB, [angle sum of a quadrilateral]. So , which gives .

    ½ mark

  4. Hence and are supplementary.

    ½ mark

Answer: , so the two angles are supplementary.

Where the marks are

  • Correct labelled figure (½ mark)
  • with reason (½ mark)
  • Angle sum of quadrilateral OAPB (½ mark)
  • Concludes (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 430/4/1 (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.