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Assertion (A): A tangent… (Class 10 Maths Basic 2023, Q19)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic 2023: question 19

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, 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): A tangent to a circle is perpendicular to the radius through the point of contact.

Reason (R): The lengths of tangents drawn from an external point to a circle are equal.

  1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) gives the correct explanation of Assertion (A).
  2. (B)Both Assertion (A) and Reason (R) are true but Reason (R) does not give the correct explanation of 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 2023 board paper, set 430/4/1.

Hints

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

Hint 1

Check each statement separately against the theorems you know.

Hint 2

Does the equality of tangent lengths prove the perpendicularity property?

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. Both statements are standard theorems, so both A and R are true.

  2. R (equal tangent lengths) does not explain why the tangent is perpendicular to the radius. Answer: option (B).

    1 mark

Answer: Option (B)

Where the marks are

  • Identifies both as true and R not explaining A (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 paper2023 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.