Ruler and Compass Construction 41
Apollonius' Problem: Circle tangent to three circles
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1. Perpendicular diameters BE, CD.
2. Midpoint F of radius AC.
3. Midpoint G of AF, quarter point of AC.
4. Circle centered at G through E.
5. Bisector GH of angle EGP.
6. Bisector GI of angle EHP.
7. Intersection J of GI and AE.
8. Ray GK at 45 degrees from GI.
9. Circle with diameter KE, center M.
10. Intersection N of circle with AC.
11. Circle centered at J, through N.
12. Perpendiculars at Q,R.
13. Two vertices S,T of the 17-gon
14. Circle centered at T through S, to give vertex U.
15. Repeating 14 more times, going around twice to get all vertices.
16. Segments between vertices give the 17-gon.