Question 73
Circles $\omega_1,\omega_2$ touch at $A$ and lie inside circle $\Omega$. Circle $\omega_1$ touches $\Omega$ at $B$ and $\omega_2$ touches it at $C$. Line $AC$ meets $\omega_1$ again at $D$. Prove that triangle $DBC$ is right-angled if $A,B,C$ are not collinear.