Question 25
A point $T$ is chosen inside triangle $ABC$. Let $A_1, B_1, C_1$ be the reflections of $T$ in the lines $BC, CA, AB$, respectively. Denote the circumcircle of triangle $A_1B_1C_1$ by $\Omega$. Let the lines $A_1T, B_1T, C_1T$ meet the circle $\Omega$ again at the points $A_2, B_2, C_2$, respectively. Prove that the lines $AA_2, BB_2, CC_2$ are concurrent, and that their common point lies on $\Omega$.