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10

Part of 2014 Sharygin Geometry Olympiad

Problems(1)

Externally Tangent Circles in an Angle Part II

Source: Sharygin Geometry Olympiad 2014 - Problem 10

11/15/2014
Two disjoint circles ω1\omega_1 and ω2\omega_2 are inscribed into an angle. Consider all pairs of parallel lines l1l_1 and l2l_2 such that l1l_1 touches ω1\omega_1 and l2l_2 touches ω2\omega_2 (ω1\omega_1, ω2\omega_2 lie between l1l_1 and l2l_2). Prove that the medial lines of all trapezoids formed by l1l_1 and l2l_2 and the sides of the angle touch some fixed circle.
geometrytrapezoidgeometry unsolved