Four Right Triangles in One

Geometry Level 3

Let ABCDABCD be a quadrilateral with AB=25,BC=39,CD=60AB = 25, BC = 39, CD = 60, and DA=52DA = 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=8:9AC : BD = 8 : 9, what is the area of quadrilateral ABCD?ABCD?

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