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Mathematics — CBSE Class 10 board question

Q1. [1]
Directions: Select the correct answer from the codes (A), (B), (C) and (D). Assertion (A): Radius is the smallest distance of a tangent from the centre of the circle. Reason (R): Radius is perpendicular to the tangent.
  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.
Previously asked in CBSE board exam
2026 30/3/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:26 · grounding rag
Model Answer

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

Since the radius is perpendicular to the tangent (Theorem 10.1), it is the shortest distance from the centre to the tangent line, making it the smallest distance.

Explanation

The key link: a perpendicular from a point to a line is always the shortest distance. Because OP ⊥ XY (Theorem 10.1), OP < OQ for every other point Q on the tangent. So R directly explains A — choose option (A).

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