Question

In an isosceles ∆ABC, if AC = BC and AB² = 2AC², then ∠C = ?
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer 1

(d) 90°

Given:
AC = BC
$A{B}^2=2A{C}^2=A{C}^2+A{C}^2=A{C}^2+B{C}^2$
Applying Pythagoras theorem, we conclude that ∆ABC is right angled at C.
or, $\angle C=90°$