$A_1$ and $A_2$ are two circles in a plane. The common external tangent to $A_1$ and $A_2$ consists of length $2017$. The common internal tangent consists of length $2009$. Find $r_1 \cdot r_2$ the product of the radii.
This is fairly complicated.
The solution uses $(r_1 - r_2)^2 + 2017^2$, but I dont see how to achieve this using the Pythagorean theorem?
$$|O_1 O_2|^2=(r_2-r_1)^2+d^2$$