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Pompeiu's Theorem Revisited

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Abstract:

Pompeiu's theorem states that if ABC is an equilateral triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B, C, and M.

Document Type: Research Article

DOI: https://doi.org/10.4169/193113409X458697

Publication date: 2009-09-01

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