Creation of this applet was inspired by a [url=http://www.gogeometry.com/problem/p774-triangle-circumcircle-altitude-tangent-parallel-plane-geometry.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? [br][/color][/b]