Suppose a circle is centered at $O$, $CD$ is a chord perpendicular to a diameter $AB$, and a chord $AE$ bisects the radius $OC$. Show that the chord $DE$ bisects the chord $BC$.
If $N$ is the middle point of $CB$, $MN$ is a middle line in $OBC$, so $MN \parallel OB$. But I can't figure out how to prove this. Can you help me, please? Thanks!