How can I find circle-circle intersection area and set of position within the intersection area?

I have a set of position on x-z plane. (x, 0, z) I will name it set A. I have two circles on x-z plane. I knows the center and radius of those circles. How can I check if those circles have intersection area or not? If those circles have intersection area. How can I find which members of set A are within those intersection areas?

two circles intersect if the distance is smaller than the sum of their radi (radiuses, what's the correct plural?). A point is in the intersection area if for both circles the point is less than the radius away.

Some sample functions:

function checkIntersect (c1pos : Vector3, c1rad : float, c2pos : Vector3, c2rad : float) : boolean {
    return (Vector3.Distance(c1pos, c2pos) <= (c1rad + c2rad));
}

function pointInIntersection(point : Vector3, c1pos : Vector3, c1rad : float, c2pos : Vector3, c2rad : float) : boolean {
    return (Vector3.Distance(point, c1pos) <= c1rad) && (Vector3.Distance(point, c2pos) <= c2rad);
}