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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.

diagram

The known data are:
points P2,P3,P4,P5
Circle C2's radius r
Angle C
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.

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