# 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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