Question 198
Let $ABC$ be triangle with the symmedian point $L$ and circumradius $R$. Construct parallelograms $ADLE$, $BHLK$, $CILJ$ such that $D, H \in AB$; $K, I \in BC$; $J, E \in CA$. Suppose that $DE$, $HK$, $IJ$ pairwise intersect at $X$, $Y$, $Z$. Prove that inradius of $XYZ$ is $\frac{R}{2}$.