Circles with Internal Tangency, Third Passes Through the Point of Tangency

Steps

1. We choose the reference circle for the inversion. Its center is chosen at the intersection point of all three circles.
2. We apply the circular inversion to the given circles. Since all of them pass through the center of the reference circle, they are transformed into lines.
3. We find circles tangent to the images of the given circles. Their centers are found using angle bisectors.
4. We invert the found circles back using the same inversion.
5. The problem has two solutions.