Question 64
Let $ABCD$ be a cyclic quadrangle, and let its diagonals, $AC$ and $BD$, cross at $X$. Let $I$ be the incenter of the triangle $XBC$, and let $J$ be the center of the circle tangent to the side $BC$ and the extensions of the sides $AB$ and $DC$ beyond $B$ and $C$, respectively. Prove that the line $IJ$ bisects the arc $BC$ of the circle $ABCD$, not containing the vertices $A$ and $D$ of the quadrangle.