Creation of this applet was inspired by a [url=https://twitter.com/gogeometry/status/790661922270183425]tweet[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url] (GoGeometry). [br][br]The circles you see are externally tangent to each other.[br]You can move any of the [b]LARGE POINTS[/b] anywhere you'd like at any time. [br][br][b][color=#0000ff]How can we formally prove what is dynamically illustrated here? [/color][/b]
Drag the [b][color=#9900ff]center of the purple circle (BIG PURPLE POINT)[/color][/b] onto the [color=#ff0000][b]red circle[/b][/color] itself. What does this cause the radius of the [color=#9900ff]purple circle[/color] to become?
Keep the [b][color=#9900ff]BIG PURPLE POINT[/color][/b] on the [b][color=#ff0000]red circle[/color][/b]. Re-slide the slider one more time. How does the action seen here compare with the dynamics [url=https://www.geogebra.org/m/zGQC9htj]seen here[/url]?