Creation of this applet was inspired by a [url=http://www.gogeometry.com/school-college/3/p1276-equilateral-triangle-internally-tangent-circle-tutoring.htm]problem[/url] posted by [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url] (GoGeometry). [br][br]The [color=#9900ff][b]purple circle[/b][/color] and the [b][color=#666666]gray circle[/color][/b] are internally tangent to each other. [br]You can move any of the [b]LARGE POINTS[/b] anywhere you'd like [b]AT ANY TIME! [br][br]How can we formally prove the phenomenon dynamically illustrated here? [/b]