Question 125
Given an obtuse isosceles triangle $ABC$ with $CA = CB$ and circumcenter $O$. The point $P$ on $AB$ is such that $AP \lt \frac{AB}{2}$ and $Q$ on $AB$ is such that $BQ = AP$. The circle with diameter $CQ$ meets $(ABC)$ at $E$ and the lines $CE$, $AB$ meet at $F$. If $N$ is the midpoint of $CP$ and $ON$, $AB$ meet at $D$, show that $ODCF$ is cyclic.