Question 65
Let $X$, $Y$, $X'$ and $Y'$ be four points on a line $l$ with the same order as written. Consider arcs $\omega_1$ and $\omega_2$ with endpoints $\{X, Y\}$ and arcs $\omega'_1$ and $\omega'_2$ with endpoints $\{X', Y'\}$ on one side of $l$ such that $\omega_1$ is tangent to $\omega'_1$ and $\omega_2$ is tangent to $\omega'_2$. Prove that the external common tangent of $\omega_1$ and $\omega'_2$ and the external common tangent of $\omega'_1$ and $\omega_2$ meet on $l$.
