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right isosceles triangle with min area wanted inscribed in right isosceles

Source: 1998 Argentina OMA L3 p5

June 11, 2020
geometryright triangleisoscelesconstructioninscribedminimumarea of a triangle

Problem Statement

Let ABCABC a right isosceles triangle with hypotenuse AB=2AB=\sqrt2 . Determine the positions of the points X,Y,ZX,Y,Z on the sides BC,CA,ABBC,CA,AB respectively so that the triangle XYZXYZ is isosceles, right, and with minimum area.
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