I'm studying up for calculus I this fall, and I found a problem I can't solve. The figure (shown in attachment) shows a circle with radius 1 inscribed in the parabola y=x^2. Find the center of the circle. So far, I have no idea. I could use the derivative to find a tangent line, then set the two distances equal to each other and solve for y, but I have no idea at what point the circle is tanget, or even if it is (at least with an analytic proof). Since I don't have the circles equation, I can't solve for points common to both equations.