2004 AIME II Problem 12

Let A B C D be an isosceles trapezoid, whose dimensions are A B=6, B C=5= D A, and C D=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.