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
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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 
are all smaller than 
. Equilateral triangles 
and 
are constructed in the exterior of 
, and 
pass through one point 
