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.
![[alogo]](alogo.png){kind=small}
Maximum area property of inscribed quadrangles ![[0_0]](Maximum_area_files/Maximum_area_0_0_0.png)
![[0_1]](Maximum_area_files/Maximum_area_0_0_1.png)
![[0_2]](Maximum_area_files/Maximum_area_0_0_2.png)
![[1_0]](Maximum_area_files/Maximum_area_0_1_0.png)
![[1_1]](Maximum_area_files/Maximum_area_0_1_1.png)
![[1_2]](Maximum_area_files/Maximum_area_0_1_2.png)