Question 106
In triangle $ABC$ with $m(\angle A) = 90^{\circ}$ we construct $AD \perp BC$ ($D \in BC$) and the bisector $AE$ ($E \in BC$). Denote by $L$ and $F$ the orthogonal projections of the point $E$ onto the legs $[AB]$ and $[AC]$. Prove that the lines $AD$, $BF$ and $CL$ are concurrent.
