Know cyclic quadrilaterals?

Geometry Level pending

In triangle ABC angle C is right with AB=12. Squares ABXY and ACWZ are constructed outside ABC. Given that the points W, X, Y, Z lie on one circle, the perimeter of ABC can be expressed in the form of a+b*sqrt(c) where c isn't divisible by the square of any prime. Find a+b+c. Source: AMC 10

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