Maximum Quadrilateral

Given segments of fixed lengths a, b, and c. Say

Construct a fourth segment d such that the resulting quadrilateral formed by the four segments has maximum area.

Alternative statement:

Proposition:  A quadrilateral ABCD for which three sides AB, BC, and CD have prescribed lengths achieves the maximal area if and only if it is cyclic and the side AD is a diameter of the circumscribed Circle.


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