In an isosceles triangle ABC, if AC=BC and `"AB"^{2}`=`"2AC"^{2}` , then the measure of angle C will be

(a) 30˚

(b) 45˚

(c) 60˚

(d) 90˚

(d) 90˚

**Explanation:**

In Isosceles △ ABC

AC = BC

∠B = ∠A (Equal Sides have equal angles opposite side to them)

⇒ ` AB^{2} ` = 2` AC^{2} `

⇒ ` AB^{2} ` = ` AC^{2} `+ ` AC^{2} `

⇒ ` AB^{2} ` = ` AC^{2} `+ ` AC^{2}`(AC = BC)

∴ ∠C = 90˚