I need to find the circle that will be tangent to a line at a given point and a circle. The diagram below hopefully makes it clearer.
The known data are:
Circle C2's radius r
The distance from P3 to P2, a
I need to find P1 or b (which makes it easy enough to work out P1). There are actually two solutions to this problem. Circle C1 could also be tangent on the far side of C2 (c=b-r).
As some background info I am using this to find the medial axis of a polygon. By stepping P3 along each line/arc of the polygon I can generate an approximation of the medial axis. I have already worked out the solution for two lines.