Question 4
In the interior of a cyclic quadrangle $ABCD$ a point $P$ is given such that
$$
|\angle BPC| = |\angle BAP| + |\angle PDC|.
$$
Denote by $E$, $F$, and $G$ the feet of the perpendiculars from the point $P$ to the lines $AB$, $AD$ and $DC$, respectively. Show that the triangles $FEG$ and $PBC$ are similar.
$$
|\angle BPC| = |\angle BAP| + |\angle PDC|.
$$
Denote by $E$, $F$, and $G$ the feet of the perpendiculars from the point $P$ to the lines $AB$, $AD$ and $DC$, respectively. Show that the triangles $FEG$ and $PBC$ are similar.