Question 150
A point $T$ is chosen inside the triangle $ABC$. Let $A_1, B_1$ and $C_1$ be the reflections of $T$ across the lines $BC, CA$ and $AB$, respectively. The lines $A_1T, B_1T$ and $C_1T$ intersect the circle $k$ circumscribed to the triangle $A_1B_1C_1$ again at $A_2, B_2$ and $C_2$, respectively.
Prove that the lines $AA_2, BB_2$ and $CC_2$ are concurrent on $k$.
(IMO Shortlist 2018)
Prove that the lines $AA_2, BB_2$ and $CC_2$ are concurrent on $k$.
(IMO Shortlist 2018)