Challenge your brain 4

Geometry Level pending

Given a point P on a triangular piece of paper ABC, consider the creases that are formed in the paper when A, B, and C are folded onto P. Let us call P a fold point of triangle ABC if these creases, which number three unless P is one of the vertices, do not intersect. Suppose that AB=36, AC=72, and angle B=90 Then the area of the set of all fold points of triangle ABC can be written in the form q(pi) - r(s^1/2) here q, r, and s are positive integers and s is not divisible by the square of any prime. What is q+r+s?

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