Creation of this applet was inspired by a [url=https://twitter.com/gogeometry/status/836566320770592769]tweet[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url]. [br][br]In this applet, the smaller circle is tangent to both the larger circle and the diameter of the larger circle. [br][br]Interact with this applet for a few minutes. [br]As you do, be sure to change the locations of any 1 (or more) of the [b]LARGER WHITE POINTS. [/b] [br][br]How can you formally prove what this applet informally illustrates? [br](For an algebraic interpretation of the [color=#9900ff][b]length of the purple segment[/b][/color], [url=https://www.geogebra.org/m/AxWhacFx]click here[/url].)