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Geometry Difficulty 4.7 AIME Find the answer

Let (x,y)(x, y) be a point in the cartesian plane, x,y>0x, y>0. Find a formula in terms of xx and yy for the minimal area of a right triangle with hypotenuse passing through (x,y)(x, y) and legs contained in the xx and yy axes.

A number or a short expression. Spacing and $ signs are ignored.

Solution

2xy2 x y.

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