Two Concentric Circles, Third Circle Intersecting One Of Them

Steps

1. Make a line f trough the joined centers of circles c and d and the center of circle e.
2. Draw circle g between the radii of circles c and d. You'll find point H, the intersection of line f and circle g.
3. Draw circle h with the center at point H going through point G, which lies on the intersection of line f and cirle g.
4. Draw the lines i, j, k, l and m. Every one is passing through the center of circle e and intersectiom of circles d and e, or e and h.
5. Draw the lines k and n, which are the axes of the angles formed by the lines i and j and l and m.
6. Draw circles p and r. These lie on the intersection of circle e with lines k and n.
7. Draw circles k₁ and k₂ which have centres at the intersections of the circle g with the lines k and n and the points O and K which lie at the intersections of the lines n and k and the circle e.
8. Circles k₁ and k₂
9. Draw an ellipse t. Its foci lie at the centers of the circles e and c and d, passing through the point S, which lies midway between points Q and R, these lying at the intersections of the line f with the circles e and d.
10. Draw a hyperbola c₁. Its foci lie at the centres of the circles e and c and d, it passes through the point W which lies midway between the points Q and T, these lie at the intersections of the line f with the circles e and c.
11. We find the intersections of the ellipse t and the hyperbola c₁ - Z and A₁, on which the centers of the resulting circles lie. From these points, draw lines to the center of the circle e, find the points B₁ and V lying on these lines and the circle e.
12. Draw the circles k₃ and k₄. Their centres lie at points A₁ and Z and pass through points V and B₁.
13. Circles k₁, k₂, k₃ and k₄.