Ruler and Compass Construction 31B
Internal Tangents to Two Given Circles

1. Ray AB
2. Perpendiculars to AB at A and B
3. Top and bottom of circles C, D
4. Ray CD; intersection E
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.
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