Question 61
On sides $BC$ and $AC$ of triangle $ABC$ lie points $D$ and $E$, respectively. Let $F$ ($F \neq C$) be the intersection of the circumcircle of triangle $CED$ and the line through $C$ parallel to $AB$. Let $G$ be the intersection of line $FD$ and side $AB$, and let $H$ be a point on line $AB$ such that $\measuredangle HDA = \measuredangle GEB$ and $H-A-B$. If $DG = EH$, prove that the intersection of segments $AD$ and $BE$ belongs to the bisector of angle $ACB$.
(Miloš Milosavljević)
(Miloš Milosavljević)