Question 7
In triangle $ABC$, we have $m(\angle A) \lt m(\angle C)$. Let $E$ be a point on the bisector of angle $B$ such that $\angle EAB = \angle ACB$. Let $D$ be a point on line $BC$ such that $B \in (CD)$ and $[BD] = [AB]$. Prove that the midpoint $M$ of the line segment $[AC]$ belongs to the line $DE$.
Bogdan Antohe
Bogdan Antohe