Question 13
C1 (NET 1), IMO 2. A scalene triangle $A_1A_2A_3$ is given with sides $a_1,a_2,a_3$ ($a_i$ is the side opposite to $A_i$). For all $i=1,2,3$, $M_i$ is the midpoint of side $a_i$, $T_i$ is the point where the incircle touches side $a_i$, and the reflection of $T_i$ in the interior bisector of $A_i$ yields the point $S_i$. Prove that the lines $M_1S_1,M_2S_2,M_3S_3$ are concurrent.