Ruler and Compass Construction 31A
External Tangents to Two Given Circles
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1. Ray AB
2. Perpendiculars to AB at A and B
3. Tops of circles C, D
4. Ray CD
5. Midpoint F of AE
6. Circle centered at F through A
7. Points of tangency G, H
8. Tangent lines EG, EH
Explanation of the construction: Steps 1-4 find the point E, the concurrent
point of all lines passing through corresponding points of the two circles.
The desired tangent lines must also pass through E. Then it is construction 27
to find the tangent lines.