Let ABC be an acute triangle and G be the intersection of the meadians of triangle ABC. Let Dbe the foot of the altitude drawn from A to BC. Draw a parallel line such that it is parallel to BC and one of the points of it is A.Donate the point S as the intersection of the parallel line and circumcircle ABC. Prove that S,G,D are co-linear
[asy]
size(6cm);
defaultpen(fontsize(10pt));
pair A = dir(50), S = dir(130), B = dir(200), C = dir(-20), G = (A+B+C)/3, D = foot(A, B, C);draw(A--B--C--cycle, black+linewidth(1));
draw(A--S^^A--D, magenta);
draw(S--D, red+dashed);
draw(circumcircle(A, B, C), heavymagenta);string[] names = {"A", "B", "C","D", "G","S"};
pair[] points = {A, B, C,D,G,S};
pair[] ll = {A, B, C,D, G,S};
int pt = names.length;
for (int i=0; i geometryJuniorAzerbaijancolinear