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GoGeometry Action 98!

Creation of this applet was inspired by a post from Antonio Gutierrez (GoGeometry). You can change the measure of the blue angle (soon to form) using the blue slider. Feel free to move the BIG ORANGE POINT (soon to appear) at any time as well. The LARGE WHITE POINTS are also moveable. How can we formally prove what is informally illustrated here?

Quick (Silent) Demo