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Mathematics — CBSE Class 10 board question

Q1. [1]
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. Select the correct answer from the codes (A), (B), (C) and (D) given below:
  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
2025 30/3/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:22 · grounding rag
Model Answer

(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

Explanation

A is true: By the RHS congruence used in Theorem 10.2's proof, △OQP ≅ △ORP, so the two tangents subtend equal angles (∠QOP = ∠ROP) at the centre.

R is true: Exercise 10.2, Q.11 establishes that a parallelogram circumscribing a circle is a rhombus (since all four sides become equal using the equal-tangent-length property).

R does not explain A: The rhombus result is an independent application of Theorem 10.2; it does not logically lead to or explain why the two tangents subtend equal angles at the centre. Hence option (B).

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