Question 94
Let $ABC$ be an acute triangle with circumcenter $O$. Let $D$ be the foot of the altitude from $A$ to $BC$ and let $M$ be the midpoint of $OD$. The points $O_{b}$ and $O_{c}$ are the circumcenters of triangles $AOC$ and $AOB$, respectively. If $AO = AD$, prove that the points $A$, $O_{b}$, $M$ and $O_{c}$ are concyclic.