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Heptagonal Triangles and Their Companions

2009
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Forum Geometricorum
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unpublished

A heptagonal triangle is a non-isosceles triangle formed by three ver-tices of a regular heptagon. Its angles are π 7 , 2π 7 and 4π 7. As such, there is a unique choice of a companion heptagonal triangle formed by three of the remaining four vertices. Given a heptagonal triangle, we display a number of interesting companion pairs of heptagonal triangles on its nine-point circle and Brocard circle. Among other results on the geometry of the heptagonal triangle, we prove that the circumcenter and

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