Four Right Triangles in One

Geometry Level 3

Let \(ABCD \) be a quadrilateral with \(AB = 25, BC = 39, CD = 60\), and \(DA = 52\), as shown above.

If the two diagonals are perpendicular to each other, yielding 4 Pythagorean triples for the 4 right triangles, and \(AC : BD = 8 : 9\), what is the area of quadrilateral \(ABCD?\)

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