Question 15
(LUX 2) Angles of a given triangle $ABC$ are all smaller than $120^\circ$. Equilateral triangles $AFB$, $BDC$ and $CEA$ are constructed in the exterior of $\triangle ABC$.
(a) Prove that the lines $AD$, $BE$, and $CF$ pass through one point $S$.
(b) Prove that $SD+SE+SF=2(SA+SB+SC)$.
(a) Prove that the lines $AD$, $BE$, and $CF$ pass through one point $S$.
(b) Prove that $SD+SE+SF=2(SA+SB+SC)$.