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Three circles touching externally

Source: Problem 2, Polish NO 1989

October 1, 2005
geometrygeometric transformationhomothetygeometry unsolved

Problem Statement

k1,k2,k3k_1, k_2, k_3 are three circles. k2k_2 and k3k_3 touch externally at PP, k3k_3 and k1k_1 touch externally at QQ, and k1k_1 and k2k_2 touch externally at RR. The line PQPQ meets k1k_1 again at SS, the line PRPR meets k1k_1 again at TT. The line RSRS meets k2k_2 again at UU, and the line QTQT meets k3k_3 again at VV. Show that P,U,VP, U, V are collinear.
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