MathDB

15

Part of 1984 IMO Shortlist

Problems(1)

Equilateral triangles in the exterior of ABC

Source:

9/8/2010
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).
geometryTriangleconcurrencyequationIMO Shortlist