Question 28
Let $ABCD$ be a parallelogram. Let $W$, $X$, $Y$, and $Z$ be points on sides $AB$, $BC$, $CD$, and $DA$, respectively, such that the incenters of triangles $AWZ$, $BXW$, $CYX$ and $DZY$ form a parallelogram. Prove that $WXYZ$ is a parallelogram.