Secant Through Center, Center as Given Point

Steps

1. If we use the given circle as the circle of inversion, the solution circles are mapped to its tangents that are parallel to the given line.
2. These tangents are then inverted back to obtain the solution circles.
3. The problem has two solutions.

Steps

1. The centers of the desired solution circles lie on the perpendicular to the given line passing through the center of the circle, which is also the point through which the solution circles must pass. The intersections of this line with the given circle are the points of tangency between the solution circles and the given circle.
2. The centers lie at the midpoints of the segments connecting the center of the given circle and the points of tangency.
3. The problem has two solutions.