Ruler and Compass Construction 35
Circle Tangent to the Inside of an Angle and Tangent to a Given Circle

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1. Circle centered at M, same radius
2. Perpendiculars to MN, MP through M
3. Perpendiculars to MB through B, and to Mc through c
4. Perpedicular to AB through D
5. Circle centered at A, radius DE
6. Perpendicular to AB through F
7. Angle bisector
8. Circle centered at E, radius FG
9. Segment AD
10. Perpendicular to AD at D
11. Circle centered at A, through H
12. Circle centered at H, radius DI
13. Perpendicular to AB at J
11. Circle centered at K, through D

Explanation of the construction: I first construct a displaced angle BAC, so
that the desired tangent circle has the same center as the tangent circle to
angle BAC and point D, so I can then use construction 34 to find the center
of that circle.