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Question

∆ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ∆ABC is a right triangle

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Solution

Given:
AC = BC
Also,AB2 = 2AC2 = AC2 + AC2 AB2 = AC2 + BC2 ( AC = BC)

It is evident that the sum of squares of the two sides of triangle ABC is equal to square of the third side.

Therefore, by applying Pythagoras theorem, we conclude that ∆ABC is right-angled at C.

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