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# ABC is an isosceles triangle with AC = BC. If $$AB^2 = 2AC^2$$, prove that ABC is a right triangle.

Given, $$\triangle$$ABC is an isosceles triangle having AC = BC and $$AB^2 = 2AC^2$$

In $$\triangle$$ ACB,
AC = BC
$$AB^2 = 2AC^2$$
$$AB^2 = AC^2 + AC^2$$
= $$AC^2 + BC^2$$ [Since, AC = BC]

Hence, by Pythagoras theorem $$\triangle$$ ABC is right angle triangle.