Ruler and Compass Construction 2
Perpendicular to Line Through Point Not on Line

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1. Arbitrary circle at C intersecting line AB
2. Circle centered at D through C
3. Circle centered at E through C
4. Lower intersection point F
5. Perpendicular line FC

Why it works:
Points E and D are equidistant from C, so C is on the perpendicular bisector of DE. And F is
constructed equidistant from D and E, so it is also on the perpendicular bisector. So CF is the
perpendicular bisector of DE, and thus the line through C perpendicular to AB.