Question 56
Let $\triangle ABC$ be an isosceles triangle with $AB = AC$ and $\angle A = 45^\circ$. Its circumcircle $(c)$ has center $O$, $M$ is the midpoint of $BC$ and $D$ is the foot of the perpendicular from $C$ to $AB$. With center $C$ and radius $CD$ we draw a circle which internally intersects $AC$ at the point $F$ and the circle $(c)$ at the points $Z$ and $E$, such that $Z$ lies on the small arc $\widehat{BC}$ and $E$ on the small arc $\widehat{AC}$. Prove that the lines $ZE$, $CO$, $FM$ are concurrent.
Brazitikos Silouanos, Greece
Brazitikos Silouanos, Greece