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February 18th, 2019, 11:13 PM   #1
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Rectangle inscribed in a circle

Is the area of a rectangle inscribed in a circle ever rational?
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February 18th, 2019, 11:41 PM   #2
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put a $1 \times 1$ square inside a circle with radius $\dfrac{1}{\sqrt{2}}$

is one of infinite examples.
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February 19th, 2019, 02:17 AM   #3
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Other than a square?
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February 19th, 2019, 02:21 AM   #4
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Mea culpa. You're right, romsek.
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February 19th, 2019, 04:42 AM   #5
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Take any rectangle with rational area. Circumscribe it by a circle. This is always possible since rectangles are cyclic quadrilaterals.
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February 19th, 2019, 08:12 AM   #6
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Quote:
Originally Posted by Loren View Post
Other than a square?
SDK has answered this but it should be clear that because the distance from the center of a rectangle to each of the corners is a constant that any rectangle can be inscribed in a circle.
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