Question 565857
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Inscribed rectangle.  The long side of the rectangle must be a chord less than a diameter.  If one side of the rectangle were a diameter, then the other long side would have to be a diameter and either that second side would have endpoints outside of the circle (hence not an inscribed rectangle) or the short sides of the rectangle would have zero length, hence no rectangle at all.


The only rectangle that can have an inscribed circle (that is the only way I can make sense of your "circumscribed rectangle") is a square because all 4 sides would necessarily have the same length.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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