Problem

The key is using Brahmagupta's formula for cyclic quadrilaterals and the extended law of sines to connect the diagonal and sides. Since you know the area, circumradius, and one side, you can find constraints on the remaining sides through the relationship between a chord, the radius, and the inscribed angle it subtends. The diagonal $BD$ acts as a chord that divides the quadrilateral into two triangles; use the law of sines in each triangle to relate the sides to the angles, then leverage the area formula to pin down $BC \cdot CD$.

The key is using Brahmagupta's formula for cyclic quadrilaterals and the extended law of sines to connect the diagonal and sides. Since you know the area, circumradius, and one side, you can find constraints on the remaining sides through the relationship between a chord, the radius, and the inscribed angle it subtends. The diagonal $BD$ acts as a chord that divides the quadrilateral into two triangles; use the law of sines in each triangle to relate the sides to the angles, then leverage the area formula to pin down $BC \cdot CD$.