Question 128
Let the incircle of triangle $ABC$ have center $I$ and touch the sides $BC$, $AC$ and $AB$ at points $D$, $E$, $F$ respectively. Let $J_1, J_2, J_3$ be the excentres opposite $A$, $B$, $C$ respectively. Let $J_2F$ and $J_3E$ intersect at $P$, $J_3D$ and $J_1F$ intersect at $Q$, $J_1E$ and $J_2D$ intersect at $R$. Show that $I$ is the circumcenter of $PQR$.