Complex Cyclic with Surprising Solution

Geometry Level 5

The circle $$S$$ has the diameter $$AB$$, which has an integer length. Points $$D$$ and $$E$$ are added on the circle to create the cyclic quadrilateral $$ADBE$$, such that $$AD$$, $$BD$$, $$BE$$ and $$AE$$ have integer lengths and the lengths of $$AE$$ and $$BD$$ are prime numbers. What is:

${ (AD-5) }^{ 2 }+{ (BD-2) }^{ 2 }+{ (AE+2) }^{ 2 } \\ +{ (BE-1) }^{ 2 }-2(AB-3)(DE-3)-18$

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