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Inscribed polygon investigation

From a question by Dave Marain, and a generalization by Pat Bellew. How can you start with a single question and get to more? From where does the idea to generalize come? This question went from show the triangle is half the hexagon, to what is the ratio of a k*m-gon to an inscribed k-gon? Dave's original post: http://mathnotations.blogspot.com/2015/07/balanced-learning-is-not-blended-or.html