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A 5-Circle Incidence Theorem

J. Chris Fisher, Larry Hoehn and Eberhard M. Schröder
Mathematics Magazine
Vol. 87, No. 1 (February 2014), pp. 44-49
DOI: 10.4169/math.mag.87.1.44
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.87.1.44
Page Count: 6
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A 5-Circle Incidence Theorem
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Abstract

Summary We state and prove a surprising incidence theorem that was discovered with the help of a computer graphics program. The theorem involves sixteen points on ten lines and five circles; our proof relies on theorems of Euclid, Menelaus, and Ceva. The result bears a striking resemblance to Miquel’s 5-circle theorem, but as far as we can determine, the relationship of our result to known incidence theorems is superficial.

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