Question 126
In triangle $ABC$ let $A_0, B_0, C_0$ be the midpoints of the sides $BC, CA, AB$, respectively, and let $A_1, B_1, C_1$ be the midpoints (by length) of the broken lines $BAC$, $CBA$, $BCA$, respectively. Prove that the lines $A_0A_1$, $B_0B_1$, $C_0C_1$ are concurrent.