Let points A, B, C, and D be the vertices on a square. Let ¯CD's midpoint be E. Flex the square into a circle (so they'll have equal perimeter/circumference), and translate the circle so it touches point E (i.e. if ¯CD is the bottom line, then translate the circle up). Prove or disprove whether the points A and B will lie inside the circle or not. Using graphing tools I've determined that points A and B do lie inside the circle, but not by much. Need a nice, simple proof though. Thanks.
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