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2019 T12: Angle-Pythagorean Quadrilaterals

Source:

January 27, 2019
2019team

Problem Statement

Call a convex quadrilateral angle-Pythagorean if the degree measures of its angles are integers w≤x≤y≤zw\leq x \leq y \leq z satisfying w2+x2+y2=z2.w^2+x^2+y^2=z^2. Determine the maximum possible value of x+yx+y for an angle-Pythagorean quadrilateral.
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