Constructing a circle through a given point, tangent to a given line, and tangent to a given circle

It is possible, provided that the point and at least part of the circle are on the same side of the line and the circle does not separate the point from the line. If the point and the circle are on opposite sides of the line, or if the point is inside the circle and the line wholly outside, then it is impossible (as it is with three nested circles in the original version).

Wikipedia describes this as Special case 6 of Apollonius' problem with up to 4 solutions