Christmas Contest - Team Round - Problem 18

Let a parabola y=x^2 and a circle \gamma share a common tangent at (1,1). If \gamma is tangent to the positive x-axis and the radius of the circle can be expressed as \frac{a-\sqrt b}{c}, where a,b,c are positive integers and b is not divisible by the square of any prime, find a+b+c.