Common External Tangents

Let $\Omega_1$ and $\Omega_2$ be two circles in the plane. Suppose the common external tangent to $\Omega_1$ and $\Omega_2$ has length $2017$ while their common internal tangent has length $2009$. What is the product of the radii of $\Omega_1$ and $\Omega_2$?

(Source: NIMO 19)