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concurrency, // diameters of 3 tangent circles (2011 Kyiv City MO Round2 11.4)

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July 31, 2020
geometryconcurrencyconcurrenttangent circles

Problem Statement

Let three circles be externally tangent in pairs, with parallel diameters A1A2,B1B2,C1C2A_1A_2, B_1B_2, C_1C_2 (i.e. each of the quadrilaterals A1B1B2A2A_1B_1B_2A_2 and A1C1C2A2A_1C_1C_2A_2 is a parallelogram or trapezoid, which segment A1A2A_1A_2 is the base). Prove that A1B2,B1C2,C1A2A_1B_2, B_1C_2, C_1A_2 intersect at one point.
(Yuri Biletsky )
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