ELMO SL 2010 G1

Let $ABC$ be a triangle. Let $A_1$ , $A_2$ be points on $AB$ and $AC$ respectively such that $A_1A_2 \parallel BC$ and the circumcircle of $\triangle AA_1A_2$ is tangent to $BC$ at $A_3$ . Define $B_3$ , $C_3$ similarly. Prove that $AA_3$ , $BB_3$ , and $CC_3$ are concurrent.

Carl Lian.