[color=#000000][b]Theorems:[/b][/color][br][br]The [b][color=#cc0000]circumcenter,[/color][/b] [color=#38761d][b]centroid,[/b][/color] and [color=#ff7700][b]orthocenter[/b][/color] of any triangle are always collinear. The line that contains these 3 points is called the triangle's [i]Euler Line[/i]. [br][br]If [color=#cc0000][b]C = circumcenter,[/b][/color] [color=#38761d][b][i]G[/i] = centroid, [/b][/color]and[color=#ff7700][b] [i]O[/i] = orthocenter,[/b][/color] then [math]\frac{CG}{CO}=\frac{1}{3}[/math]. [br]