IMO Shortlist 1984 problem 15
Dodao/la:
arhiva2. travnja 2012. Angles of a given triangle
are all smaller than
. Equilateral triangles
and
are constructed in the exterior of
.
(a) Prove that the lines
, and
pass through one point
(b) Prove that
%V0
Angles of a given triangle $ABC$ are all smaller than $120^\circ$. Equilateral triangles $AFB, BDC$ and $CEA$ are constructed in the exterior of $ABC$.
(a) Prove that the lines $AD, BE$, and $CF$ pass through one point $S.$
(b) Prove that $SD + SE + SF = 2(SA + SB + SC).$
Izvor: Međunarodna matematička olimpijada, shortlist 1984
Školjka 
