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Assertion (A): The tangents… (Class 10 Maths 2024, Q19)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2024: question 19

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedCircles

Assertion (A): The tangents drawn at the end points of a diameter of a circle, are parallel.

Reason (R): Diameter of a circle is the longest chord.

  1. (A)Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
  2. (B)Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for 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 2024 board paper, set 30/1/1.

Hints

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

Hint 1

What is the angle between a tangent and the radius at the point of contact?

Hint 2

Check whether 'longest chord' is actually used in proving the lines are parallel.

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. Assertion: each tangent is perpendicular to the radius at its point of contact, so both tangents are perpendicular to the same diameter. Hence they are parallel, and A is true.

  2. Reason: the diameter is indeed the longest chord, so R is true. However, the parallelism comes from 'tangent ⟂ radius', not from the diameter being longest. So R does not explain A, and the answer is option (B).

    1 mark

Answer: Option (B)

Where the marks are

  • Judges both statements true, with R not explaining A, option (B) (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 paper2024 board paper, set 30/1/1 (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.