Question 32
Circles $\Omega_1$, centre $Q$, and $\Omega_2$, centre $R$, touch externally at $B$. A third circle, $\Omega_3$, which contains $\Omega_1$ and $\Omega_2$, touches $\Omega_1$ and $\Omega_2$ at $A$ and $C$, respectively. Point $C$ is joined to $B$ and the line $BC$ is extended to meet $\Omega_3$ at $D$.
Prove that $QR$ and $AD$ intersect on the circumference of $\Omega_1$.
Prove that $QR$ and $AD$ intersect on the circumference of $\Omega_1$.