Question 58
Point $H$ is the orthocenter of a triangle $ABC$ and segments $AD$, $BE$, $CF$ are its altitudes. Points $I_1$, $I_2$, $I_3$ are incenters of triangles $EHF$, $DHF$, $DHE$, respectively. Prove that lines $AI_1$, $BI_2$, $CI_3$ intersect at one point.