GoGeometry Action 8!

Creation of this applet was inspired by a [url=https://twitter.com/gogeometry/status/839587229869699082]tweet[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url]. [br][br]The [color=#bf9000][b]two smaller circles[/b][/color] you see are tangent to each other and are also tangent to the [color=#6aa84f][b]largest circle[/b][/color]. [br][br][b][color=#0000ff]How can you formally prove what this applet informally illustrates? [/color][/b]

Information: GoGeometry Action 8!