Let be a convex pentagon such that , , and . Prove that the perpendicular line from to and the line segments and are concurrent.
Let $ABCDE$ be a convex pentagon such that $AB=BC=CD$, $\angle{EAB}=\angle{BCD}$, and $\angle{EDC}=\angle{CBA}$. Prove that the perpendicular line from $E$ to $BC$ and the line segments $AC$ and $BD$ are concurrent.
Školjka 
be a convex pentagon such that 
, 
, and 
. Prove that the perpendicular line from 
to 
and the line segments 
and 
are concurrent.