KöMaL 2015 B4754

Lines $AD$ , $BD$ and $CD$ passing through an interior point $D$ of a triangle $ABC$ intersect the opposite sides at $A_{1}$, $B_{1}$ and $C_{1}$, respectively. The midpoints of the segments $A_1B_1$, $B_1C_1$ and $C_1A_1$ are $C_2$, $A_2$ and $B_2$, respectively. Show that the lines $AA_{2}$, $BB_{2}$ and $CC_{2}$ are concurrent.