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Marion's Theorem

From Mathematics Learning FB Page: "Marion's Theorem, also known as Marion Walter's Theorem, states that if you trisect each side of a triangle and connect each trisection point to the opposite vertex, the area of the resulting hexagon in the middle of the triangle is one-tenth the area of the original triangle. This theorem was named after Marion Walter, who discovered it while experimenting with Geometer's Sketchpad with a colleague. Today ( July 30) is 97th BIRTHDAY Anniversary to Marion Walter." I wanted to see for other ratios, so this applet! 1/5th and 1/12th are also nice values. What's the pattern?