SUBIECTUL III

(7p)Consider the triangle $A B C, A E$ the bisector of $\angle B A C$, such that [AE] $\equiv[E C]$. Find the measure of $\angle A B C$ if $A C=2 A B$.
## SUBJECT III

Draw $E F \perp A C$ (2p); $\square E A C$ is isosceles (1p); $\Rightarrow[E F] \equiv[F C] \equiv[F A]$ (1p); $A B=\frac{A C}{2} \Rightarrow[E F] \equiv[A B]$ (1p); $\square A B E \equiv \triangle A F E(L . U . L)$ (1p); $m(\square B)=90^{\circ}$ (1p).