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ITAMO 2018 problem 2

Source:

May 9, 2018
geometry

Problem Statement

2.2.Let ABCABC be an acute-angeled triangle , non-isosceles and with barycentre GG (which is , in fact , the intersection of the medians).Let MM be the midpoint of BCBC , and let Ω be the circle with centre GG and radius GMGM , and let NN be the point of intersection between Ω and BCBC that is distinct from MM.Let SS be the symmetric point of AA with respect to NN , that is , the point on the line ANAN such that AN=NSAN=NS.
Prove that GSGS is perpendicular to BCBC
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