Let \(ABCD\) be an isosceles trapezoid, whose dimensions are \(AB = 6, BC=5=DA,\)and \(CD=4.\) Draw circles of radius 3 centered at \(A\) and \(B,\) and circles of radius 2 centered at \(C\) and \(D.\) A circle contained within the trapezoid is tangent to all four of these circles. Its radius is \(\frac{-k+m\sqrt{n}}p,\) where \(k, m, n,\) and \(p\) are positive integers, \(n\) is not divisible by the square of any prime, and \(k\) and \(p\) are relatively prime. Find \(k+m+n+p.\)

(第二十二届AIME2 2004 第12题)