Ruler and Compass Construction 36
Circle Tangent to a Line and Through Two Points

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1. Line AB
2. Perpendicular to AB at midpoint D of AB
3. Midpoint E of AC
4. Circle centered at E, through C
5. Perpendicular to AB at B
6. Circle centered at C, through F
7. Perpendicular to the original line at G
8. Circle centered at H, through A

Explanation of the construction: The Secant-Tangent Theorem says CH^2 = CB*CA, so construction 24 is used to
construct length CH.