Ruler and Compass Construction 28
Circle of Given Radius Tangent to Two Given Circles

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1. Arbitrary point E on first circle
2. Ray CE
3. Point G on ray CE so EG=AB
4. Circle centered at C, through G
5. Arbitrary point F on second circle
6. Ray DF
7. Point H on ray DF so FH = AB
8. Circle centered at D, through H
9. Intersections I,J are centers of the tangent circles
10. Tangent circles centered at I and J of radius AB

Why it works:
The center of the desired circle must be distance the sum of the two radii from the center of the first
circle, and distance the sum of the two radii from the center of the second circle, so we draw
circles of those sum distances and find their intersection.