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Determine the radius of k

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September 8, 2010
geometrytrigonometrycirclesradiusIMO Shortlist

Problem Statement

Inside triangle ABCABC there are three circles k1,k2,k3k_1, k_2, k_3 each of which is tangent to two sides of the triangle and to its incircle kk. The radii of k1,k2,k3k_1, k_2, k_3 are 1,41, 4, and 99. Determine the radius of k.k.
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