Question 109
A right triangle $ABC$, with $\angle BAC = 90^\circ$, is inscribed in the circle $\Gamma$. The point $E$ lies in the interior of the arc $\widearc{BC}$ (not containing $A$), with $EA \gt EC$. The point $F$ lies on the ray $EC$ with $\angle EAC = \angle CAF$. The segment $BF$ meets $\Gamma$ again at $D$ (other than $B$). Let $O$ denote the circumcenter of the triangle $DEF$. Prove that the points $A$, $C$, $O$ are collinear. (Posed by Bian Hongping)
