For some positive real number r, the line x + y = r is tangent to the circle x^2 + y^2 = 2r. Find r.
Note that this means that for any value of r, the two equations must have only one solution. You know that y = r - x, so x^2+(r-x)^2=2r. Expand this, create a quadratic in terms of x, and set the discriminant to be 0. That should give you r.