Question 73
Two circles $\Omega_1$ and $\Omega_2$ intersect at $A$ and $B$. From any point $P$ on $\Omega_1$ straight lines are drawn through $A$ and $B$ meeting $\Omega_2$ again at $E$ and $F$, respectively. Prove that the length of the line segment $EF$ is the same for all $P$ on $\Omega_1$.