Question 124
the incircle $k$ of $\triangle ABC$ is tangent to the sides $AB$, $BC$ and $CA$ at points $C_1$, $A_1$ and $B_1$, respectively. The points $C_2$, $A_2$ and $B_2$ are diametrically opposite to $C_1$, $A_1$ and $B_1$ in $k$.
a) Prove that the lines $AA_2$, $BB_2$ and $CC_2$ are concurrent.
b) If the line $AA_2$ meets $k$ at $A_3$, find the ratio in which the tangent line to $k$ at $A_3$ divides $BC$.
a) Prove that the lines $AA_2$, $BB_2$ and $CC_2$ are concurrent.
b) If the line $AA_2$ meets $k$ at $A_3$, find the ratio in which the tangent line to $k$ at $A_3$ divides $BC$.