Question 76
Let $ABC$ be a triangle not isosceles at $B$. Let $D$ be the foot of the bisector of $\widehat{ABC}$. Let $M$ be the midpoint of arc $\widehat{AC}$ containing $B$ on the circumcircle of $ABC$. The circumcircle of $BDM$ meets segment $[AB]$ at $K$ distinct from $B$. Reflect $A$ in $K$ to obtain $J$. Line $(DJ)$ meets $(AM)$ at $O$. Prove that $J$, $B$, $M$ and $O$ are concyclic.