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)