Analytical Geometry Problem

[JPJ]

Denote by D the domain ( (x,y) I x>= 0, y>= 0 )

Assume that a circle C contained in D touches the parabola y=(x^2)/2 at the point (2,2) and also touches the x-axis. Find the radius of C.

 

[JPJ]

Variables:
- Center C (Xc;Yc) of the circle;
- Intersection point P (2;2) between the parabole and the circle;

Strategy:
- Set up distance equation: PC = Yc = Radius, but end up with 2 variables -> R^2 = (Xc - 2)^2 + (R - 2)^2 (I). Can't find an equation that relates Xc and Yc = R, in order to solve (I) for only one variable, R.

Anyone?