Ruler and Compass Construction 37
Circle tangent to a line and a circle, and through a point.

Reset. Line LM, circle BC, point A.
1. Line through B, perpendicular to LM.
2. Midpoint F between circle and line.
3. Line FZ through F parallel to LM.
4. Expanded circle, centered at B, through F.
5. Point A expanded by same amount.
6. Inversion circle centered at F, arbitrary radius.
7. Inversion of circle BF to line HI.
8. Ray FA, with intersections J,K.
9. Inversions of J and K to P and Q
10. Midpoint R of P and Q is center of inverted circle.
11. Midline between lines HI and FZ.
12. Circle centered at R, radius sum of PR and FY.
13. Circle centered at S,radius FY, tangent to circle RP.
14. Ray FS, with intersections T,U.
15. Inversions V,W of T,U.
16. Midpoint X of T,U.
17. Circle centered at X through A. Tangent to original line and circle.
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