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)