Point on Circle, Center and Point on Same Perpendicular to Line

Steps

1. The given point and the center of the given circle lie, by construction, on the perpendicular to the given line. The foot of this perpendicular is also the point of tangency between the line and the solution circle.
2. The center of the solution circle lies at the midpoint between the given point and the point of tangency.
3. The problem has a unique solution.