[alogo] Maximal Rectangle in Circle

Inscribe in a given circle of radius R a rectangle with maximal area. Find the solution through the graph of the appropriate function.

<functions > y1 = x*sqrt(4*R^2 - x^2)
<rparameters > R = 1.5
<nparameters > nrPts = 150
<intervals > [ -2*R, 2*R ]
<nrofpoints > nrPts
<comments > Area of rectangle of one side = x, inscribed in circle of radius R.

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The function x*sqrt(4*R^2 - x^2) gives the area of the recangle inscribed in the circle with radius R, for x = |BC|. The solution is obtained for x = sqrt(2)*R, and is the inscribed square. A variant of a problem of Kepler (see KeplerProblem.html ). Proposed by Roni Levy in the third Calgeo meeting.

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