The 3 Wisemen

Geometry Level 4

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?


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