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It must be an isoseles triangle, which is composed of two right triangles. Each hypotenuse is = sqrt(1/2x^2 + y^2).
If the point is moved the hypotenuse becomes = sqrt(1/2x^2 + y^2 - 2xy*Cos(a)). Since any movement away from an isoseles triangle adds a term which reduces the length of the hypotenuse, it must be the largest triangle.
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