Question 34
Let $ABCD$ be a convex quadrilateral. Assume that the incircle of triangle $ABD$ is tangent to $\overline{AB}$, $\overline{AD}$, $\overline{BD}$ at points $W$, $Z$, $K$. Also assume that the incircle of triangle $CBD$ is tangent to $\overline{CB}$, $\overline{CD}$, $\overline{BD}$ at points $X$, $Y$, $K$. Prove that quadrilateral $WXYZ$ is cyclic.