IMO Shortlist 1984 problem 18

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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.
Izvor: Međunarodna matematička olimpijada, shortlist 1984