Math - Gravity Circle

What is the Gravitational attraction of a Circle of constant density and mass M on a point mass? 

In particular, since the circle is perfectly symmetrical,  is the gravitational attraction the same as if the entire mass of the Circle (M) were concentrated at its center? 

Below is a plot of the Gravitational Attraction experienced by the point mass.
Notice that it is zero when the point mass is at the center of the circle.
The force reaches a maximum at a certain distance, then tapers off with increasing distance from the circle.