Ruler and Compass Construction 13
Circumcircle of a given triangle

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1. Arc centered at A of arbitrary radius
2. Arc centered at B of same radius
3. Perpendicular bisector DE of AB
4. Arc centered at A of arbitrary radius
5. Arc centered at C of same radius
6. Perpendicular bisector FG of AC
7. Center of circumcircle O
8. Circumcircle centered at O

Why it works:
AB and AC are chords of the desired circle, and the construction makes the perpendicular bisectors
of the chords, which meet at the center of the circle.