The Number of Halving Circles

  title={The Number of Halving Circles},
  author={Federico Ardila},
  journal={The American Mathematical Monthly},
1. INTRODUCTION. We say that a set S of 2n + 1 points in the plane is in general position if no three of the points are collinear and no four are concyclic. We call a circle halving with respect to S if it has three points of S on its circumference, n − 1 points in its interior, and n − 1 in its exterior. The goal of this paper is to prove the following surprising fact: any set of 2n + 1 points in general position in the plane has exactly n 2 halving circles. Our starting point is the following… CONTINUE READING

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  • G. Perz
  • Crux Mathematicorum
  • 2003
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  • R. Honsberger
  • Mathematical Association of America,
  • 1978

The Chinese Mathematical Olympiads

  • F. Swetz
  • 1972
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