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 $SD + SE + SF = 2(SA + SB + SC).$
Školjka