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Van Aubel Action!!!

Creation of this applet was inspired by a Twitter tweet from Solve My Maths. The following illustration dynamically illustrates Van Aubel's Theorem. This theorem holds true for ALL QUADRILATERALS (convex and concave). So, feel free to put the BIG ORANGE VERTICES anywhere you'd like (prior to sliding the slider). How can you formally prove what this applet informally illustrates?

Quick (Silent) Demo