The 3 WisemenGeometry Level 3
Once upon a time, Ptolemy drew 2 red perpendicular lines of length \(AC = 56\) and \(BD = 63\) and said, "This is a special intersection as the lengths from point \(E\) to other vertices are all in integers."
Brahmagupta then drew 4 blue lines, connecting the vertices, and created a quadrilateral. "This is a unique quadrilateral," he claimed, "as the 4 side lengths are all in integers."
Finally, Parameshvara drew a circle, circumscribing that quadrilateral before declaring, "This is a wonderful circle, for its diameter also has the length in integer."
What is the length of this circumcircle's diameter according to these 3 wisemen?