MathNet 1985 — Part 01 Question 36

The points $A$, $B$, $C$, $D$, $E$, $F$ are equally spaced on the circumference of a circle (in that order) and $AF$ is a diameter. The center is $O$. $OC$ and $OD$ meet $BE$ at $M$ and $N$ respectively. Show that $MN + CD = OA$.