Question 28
Let $ABC$ be a triangle, and let $X, Y, Z$ be the excenters opposite $A, B, C$. The incircle of triangle $ABC$ touches $BC, CA, AB$ at points $D, E, F$. Finally, let $I$ and $O$ denote the incenter and circumcenter of triangle $ABC$.
Prove that lines $DX, EY, FZ, IO$ are concurrent.
Prove that lines $DX, EY, FZ, IO$ are concurrent.