Question 136
Let $ABC$ be a triangle with $AB \neq BC$; and let $BD$ be the internal bisector of $\angle ABC$, $(D \in AC)$. Denote by $M$ the midpoint of the arc $AC$ which contains point $B$ in the circumscribed circle of the triangle $ABC$. The circumscribed circle of the triangle $\triangle BDM$ intersects the segment $AB$ at point $K \neq B$. Let $J$ be the reflection of $A$ with respect to $K$. If $DJ \cap AM = \{O\}$, prove that the points $J$, $B$, $M$, $O$ belong to the same circle.