KöMaL 2016 B4816

Let $O$ denote the midpoint of line segment $AB$, and let $C$ be the point on line segment $OB$ for which $\frac{AO}{OC}=\frac{OC}{CB}$. Point $D$ is one of the points where the perpendicular drawn at point $C$ to $AB$ intersects the Thales circle of $AB$. Points $E$ and $F$ are the two intersections of line $AD$ with the circle of radius $OC$ centred at $O$. Determine the size of the angle $EOF$.