Question 145
Let $A$ be a point on a circle with center $O$ and $B$ be the midpoint of $[OA]$. Let $C$ and $D$ be points on the circle and on the same side of $OA$ satisfying the condition $\overline\{CBO\} = \overline\{DBA\}$. Show that the symmetric point of the midpoint of $[CD]$ with respect to the point $B$ is on the circle.