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Mascheroni construction: Construct the circumcircle of a triangle ABC with compass alone.

Given the points A,B, and C, construct the circumcircle of triangle ABC with compass alone.
Solution: In the figure below, we proceed in 10 steps. Prove that circle 10 with center L is the circumcircle of the triangle ABC.


Mascheroni construction: circumcircle 

Mascheroni or Mohr-Mascheroni Construction A geometric construction done with a movable compass alone, named after the Italian geometer Lorenzo Mascheroni (1750-1800), who, in his Geometria del compasso (1797), astonished the mathematical world by showing how every compass-and-straightedge construction can be done just using a compass without a ruler.

Straight line: it's assumed that two points, obtained by arc intersections, define a straight line.

Georg Mohr (1640-1697) proved the same results earlier in his Euclides danicus (1672).

Mascheroni, or Mohr-Mascheroni, constructions are today primarily of interest to puzzle enthusiasts who try to improve on the older solutions by finding ones with fewer steps.

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