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

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Solution

Given that
AB² = 2AC²
⇒ AB² = AC² + AC²
⇒ AB² = AC² + BC² [ Since BC = AC (given)]

Thus, the triangle satisfies Pythagoras' theorem.
Hence, the given triangle is a right-angled triangle.

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