Question 11
G5 (FRA). Let $ABC$ be a triangle, $\Omega$ its incircle and $\Omega_a,\Omega_b,\Omega_c$ three circles three circles orthogonal to $\Omega$ passing through $B$ and $C$, $A$ and $C$, and $A$ and $B$ respectively. The circles $\Omega_a,\Omega_b$ meet again in $C'$; in the same way we obtain the points $B'$ and $A'$. Prove that the radius of the circumcircle of $A'B'C'$ is half the radius of $\Omega$.