Question 57
Let $ABCD$ be a rectangle with $BC=2AB$. Let $E$ be the midpoint of $BC$ and let $P$ be any point in the interior of side $AD$. Let $F,G$ be the feet of the perpendiculars from $A$ to $BP$ and from $D$ to $CP$, respectively. Given $\angle BPC=85^\circ$:
a) Prove that triangles $BEF$ and $BEP$ are similar.
b) Find $\angle BEF+\angle CEG$.
a) Prove that triangles $BEF$ and $BEP$ are similar.
b) Find $\angle BEF+\angle CEG$.