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Equilateral triangles in the exterior of ABC

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September 8, 2010
geometryTriangleconcurrencyequationIMO Shortlist

Problem Statement

Angles of a given triangle ABCABC are all smaller than 120āˆ˜120^\circ. Equilateral triangles AFB,BDCAFB, BDC and CEACEA are constructed in the exterior of ABCABC.
(a) Prove that the lines AD,BEAD, BE, and CFCF pass through one point S.S.
(b) Prove that SD+SE+SF=2(SA+SB+SC).SD + SE + SF = 2(SA + SB + SC).
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