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GoGeometry Action 116!

Creation of this applet was inspired by a tweet from Antonio Gutierrez (GoGeometry). The circles you see are externally tangent to each other. You can move any of the LARGE POINTS anywhere you'd like at any time. How can we formally prove what is dynamically illustrated here?


Drag the center of the purple circle (BIG PURPLE POINT) onto the red circle itself. What does this cause the radius of the purple circle to become?


Keep the BIG PURPLE POINT on the red circle. Re-slide the slider one more time. How does the action seen here compare with the dynamics seen here?

Quick (Silent) Demo