Given the side-lengths a, b, c and d, the maximum area quadrangle with these data is inscribable in a circle (c). The scheme here shows how the area depends on the angle <(BAD). The graph of the function (area=f(angle)) depends on the side-lengths a, b, c and d. Modifying these side-lengths modifies also the graph. The maximum however occurs always, when the circle (c), passing through points A, B and D, passes also through D. The graph shows some irregularities due to the fact that not all angles <(BAD) lead to quadrangle constructions.

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