IMO 1984 - Shortlisted Problems Question 18

(USA 5) Inside triangle $ABC$ there are three circles $k_1,k_2,k_3$ each of which is tangent to two sides of the triangle and to its incircle $k$. The radii of $k_1,k_2,k_3$ are $1$, $4$, and $9$. Determine the radius of $k$.