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GoGeometry Action 119!

Author:
Tim Brzezinski
Topic:
Geometric Mean, Means
Creation of this applet was inspired by a tweet from Antonio Gutierrez (GoGeometry). You can control the size of the pink angle by adjusting the pink slider. You can move any of the LARGE POINTS anywhere you'd like at ANY TIME. How would you describe the phenomenon dynamically illustrated here? How can we formally prove this true?
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