Substitution in Systems of Nonlinear Equations

Let C be the circle $(x-3)^2 + (y-3)^2 = 6$ in the plane. The slopes of the points on C form a real interval $[m,M]$ (so that $m$ is the smallest slope of any point on C, and $M$ is the largest slope). What is the average value $\frac{m+M}{2}$?