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Assertion (A): If two tangents… (Class 10 Maths 2025, Q20)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/3/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2025: question 20

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedCircles

Assertion (A): If two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre of the circle.

Reason (R): A parallelogram circumscribing a circle is a rhombus.

  1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  3. (C)Assertion (A) is true, but Reason (R) is false.
  4. (D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

Join centre to the external point and points of contact.

Hint 2

Is the rhombus fact used in proving A?

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. A is true: (RHS), so .

    ½ mark

  2. R is true (equal tangents make adjacent sides equal), but it is a separate result and does not explain A. Option (B).

    ½ mark

Answer: Option (B)

Where the marks are

  • A true via congruent triangles (½ mark)
  • R true but not explanation (½ 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 paper2025 board paper, set 30/3/1 (Standard): 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.