Finding the intersecting points on two circles

Given 2 circles on a plane, how do you calculate the intersecting points?

In this example I can do the calculation using the equilateral triangles that are described by the intersection and centres of the 2 circles, however, I need a more general formula that will provide the coordinates of the 2 intersection points C and D, on circles that are not placed so conveniently, or of the same radius.

Each circle can be described by an equation of the form $(x-h)^2+(y-k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is its radius. Given the equations of the two circles, expanding the squared terms and subtracting the equations should yield an equation of the line through the two points of intersection. Solving that for $x$ or $y$ and substituting into one of the original circle equations should yield the coordinates of your two points of intersection.