Two Tangent Circles Of The Same Size, Point Is Colinear With Both Centres

Steps

0. The circles "a" and "b" and the point "C" which lies on the line of their centres are given.
1. Construct a random circle with centre at point "C".
2. Perform the circular inversion of circles "a" and "b" according to this circle.
3. Construct the tangents of the resulting circles.
4. Perform the circular inversion of the tangents according to the first circle.
5. The solutions are the circles "k₁", "k₂" and "k₃".

Steps

1. Construct points E and F, which are the intersections of circles a and b and the segments AD and BD.
2. Construct points H and G, which are the midpoints of segments ED and FD.
3. Construct hyperbolas, the loci, with foci at points B and D passing through point G, and with foci at points A and D passing through point H.
4. The circles with centers lying at the intersections of hyperbolas must pass through point D. Construct these circles.
5. k1, k2, k3 are the solution.