Point on One of Two Intersecting Circles, Inside the Other

Steps

1. Choose the circle of inversion so that its center is at the given point.
2. Apply the inversion to both given circles. One of them transforms into another circle, and the second one into a line.
3. In the chosen inversion, the solution circles are mapped to tangents to the image of the circle that are parallel to the line, which is the image of the second circle.
4. Invert the found tangents back to obtain the solution circles.
5. The problem has two solutions.