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 $$\angle B=90^\circ.\,$$ Then the area of the set of all fold points of $$\triangle ABC\,$$ can be written in the form $$q\pi-r\sqrt{s},\,$$ where $$q, r,\,$$ and $$s\,$$ are positive integers and $$s\,$$ is not divisible by the square of any prime. What is $$q+r+s\,$$?

(第十二届AIME1994 第15题)