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GoGeometry Action 147!

Creation of this applet was inspired by a tweet posted by Antonio Gutierrez (GoGeometry). You can move the LARGE WHITE VERTICES of the triangle ANYWHERE you'd like. You can also move the LARGE RED POINT anywhere on the left side of this triangle. The small gray slider controls the size of the (soon-to-appear) gray angle. How can we formally prove what is dynamically illustrated here?

Quick (Silent) Demo