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Question

# Assertion (A) In an isosceles ∆ABC, if ∠C = 90°, then AB2 = 3AC2. Reason (R) In an isosceles ∆ABC, if AC = BC and AB2 = 2AC2, then ∠C = 90°. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A) (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true.

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Solution

## (d) Assertion (A) is false and Reason (R) is true. In triangle ABC, let BC be equal to AC. We have: $\angle C=90°$ Thus, $A{B}^{2}=A{C}^{2}+B{C}^{2}=A{C}^{2}+A{C}^{2}\left(\because AC=BC\right)\phantom{\rule{0ex}{0ex}}⇒A{B}^{2}=2A{C}^{2}\phantom{\rule{0ex}{0ex}}$ Assertion (A) is false. This proves that Reason (R) is true. Hence, Assertion (A) is false and Reason (R) is true.

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