If , the regions and will not be half-planes, but the interior and exterior of a circle.

First, you have to locate two points and on the line joining and , so that and . One of these points, , will be on the line segment between and , dividing it in the ratio to . The other point, , will be on the far side of (if ), and on the far side of (if ).

Next, construct a circle for which the line segment from to is a diameter. If then will be the region outside this circle. If then it will be the region inside the circle.