Question

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

Answer 1

It is given that in $∆\mathrm{ABC}$, AC = BC
Also, it is given that AB² = 2AC^{2
$$\begin{gathered} \Rightarrow {\mathrm{AB}}^2={\mathrm{AC}}^2+{\mathrm{AC}}^2 \\ \Rightarrow {\mathrm{AB}}^2={\mathrm{AC}}^2+{\mathrm{BC}}^2(\mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{AC}=\mathrm{BC}) \end{gathered}$$}
This is a condition for the Pythagoras theorem.
Therefore, $∆\mathrm{ABC}$ is a right angled triangle, where AB is the hypotenuse and AC and BC are the other sides.
$\Rightarrow \angle \mathrm{C}={90}^{\circ }$
Hence, correct answer is option (c).