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Ellipse's Circumscribed Perimeter

Around an ellipse of eccentricity e=0.85e = 0.85 circumscribe a quadrilateral with minimum perimeter and vertices on the major and minor axes of the ellipse.

If the area of the ellipse is A1A_1 and the area of the quadrilateral is A2A_2, find A1A2×100\dfrac{A_1}{A_2}\times 100.

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