Creation of this applet was inspired by a [url=https://twitter.com/gogeometry/status/942558698383257600]tweet[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url] (GoGeometry). [br][br]Shown below is a triangle with its incircle drawn. [br]The 3 smaller circles are tangent to the larger circle and are tangent to the sides of the triangle as well.[br]The radii of these circles are shown as colored segments. [br][br]Feel free to move the vertices of the triangle anywhere you'd like. [br][br][b][color=#0000ff]How can we formally prove what is dynamically being illustrated here? [/color][/b]