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An Isosceles Mystery

David Marain (, @dmarain) shared an angle chasing puzzle in the 80-80-20 isosceles triangle. Quite a nice one. I chased a bit, then modeled in GeoGebra. Then I made a tool for making an ASA triangle which was handy for making angle chasing problems. Then I generalized the problem, and found that the 80-80-20 triangle had lots of neat situations that other triangles do not. Is there something that makes this triangle special? Tumblr post with several examples: