Euler Line Surprise! = GoGeometry Action 54

Creation of this applet was inspired by a [url=http://www.gogeometry.com/problem/p761-triangle-60-degrees-euler-line-equilateral-high-school-college.htm]post[/url] from Antonio Gutierrez ([url=http://www.gogeometry.com/]GoGeometry[/url]). [br][br][b][color=#0000ff]How can we formally prove what this applet informally illustrates? [/color][/b]

Information: Euler Line Surprise! = GoGeometry Action 54