Question 1
In the triangle $ABC$ with $AC\gt AB$, $D$ is the foot of the perpendicular from $A$ onto $BC$ and $E$ is the foot of the perpendicular from $D$ onto $AC$. Let $F$ be the point on the line $DE$ such that $EF\cdot DC=BD\cdot DE$. Prove that $AF$ is perpendicular to $BF$.