Question 30
Consider the isosceles triangle $ABC$, with $m(\angle BAC) = 100^\circ$. Let $BD$ be the angle bisector of the angle $\widehat{ABC}$, with $D \in (AC)$, the point $E \in BD$ such that $D \in (BE)$ and $BE = BC$, and the point $F \in (BC)$ such that $AB = BF$. Prove that the lines $AC$ and $EF$ are orthogonal.
