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Question

ΔACB is an isosceles triangle such that AC=BC. If AB2=2AC2, prove that ΔACB is a right angled triangle.

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Solution

ACB is an isosceles triangle ...Given
In order to prove ACB is right angled, we must prove C=90o
And AB2=2AC2
AB2=AC2+AC2
AB2=AC2+BC2 ...[AC=BC]
ACB=90o ....[Converse of Pythagoras theorem]
ΔACB is a right angled triangle.

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