How do I calculate the x, y, & z coordinates of the two points where a sphere intersects a circle? The coordinates of the center of both are known and the radii are known.
The center of the circle and the center of the sphere are not the same point.
The circle and the sphere are not tangent to each other.
The center of the sphere is not on the perpendicular through the center of the circle. I.e., the solution is not the circle, only two points.
You may orient the circle as a rotation around an axis (but the sphere is not on the axis of rotation of course).