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# ABC is an isosceles triangle right angled at C. Prove that $$AB^2 = 2AC^2$$.

Answer :

Given, $$\triangle$$ ABC is an isosceles triangle right angled at C.

In $$\triangle$$ ACB, Angle C = 90°
AC = BC (By isosceles triangle property)
$$AB^2 = AC^2 + BC^2$$ [By Pythagoras theorem]
= $$AC^2 + AC^2$$ [Since, AC = BC]
$$AB^2 = 2AC^2$$