Both Points Inside A Circle

Steps

1. Construct a circle for the inversion: select the centre of it at one of the points from the assignment, then select the radius, so that the second point lies on the circle.
2. Project the circle from the assignment through the circle from step 1 using a circular inversion.
3. Construct tangents from the point that lies on the circle (from step 1) and the projected circle (these two lines automatically passes through the last projected point, because the point is at infinity).
4. Project these tangents over the circle from step 1 using a circular inversion.
5. The projected tangents appear to be circles - the two solutions of the assignment.

Steps

1. Construct the axis of points A and B.
2. Draw a line through points A and S.
3. Name the intersections of the line with the given circle k E and F.
4. Find the centres of the line segments EA and FA.
5. These points are the extreme points of the major axis of the ellipse p, the focuses being points A and S.
6. Find the intersections of the ellipse and the axis from point 1.
7. These intersections are the centers of the resulting circles.