Creation of this applet was inspired by a [url=http://gogeometry.com/school-college/4/p1343-triangle-excircle-tangent-90-degree.htm]post[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url] (GoGeometry). [br][br]Feel free to move any 1 (or more) the [b]LARGE POINTS[/b] at any time. [br]You can adjust the size of the triangle's interior angle with gray vertex by using the gray slider. [br][br][b][color=#ff00ff]How can we prove both phenomena dynamically displayed here? [/color][/b]