KöMaL 2015 B4743

The inscribed circle of triangle $ABC$ touches sides $BC$ , $AC$ and $AB$ at points $A_1$, $B_1$ and $C_1$, respectively. Let the orthocentres of triangles $AC_1B_1$, $BA_1C_1$ and $CB_1A_1$ be $M_A$, $M_B$ and $M_C$, respectively. Show that triangle $A_1B_1C_1$ is congruent to triangle $M_AM_BM_C$.