Vecten's Collinearity: What is it about?
A Mathematical Droodle

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Copyright © 1996-2018 Alexander Bogomolny

The following curious fact has been communicated to me by Professor Ricardo Barroso Campos from the University of Sevilla, Spain.

In any triangle, the two Vecten points and the center of the 9-points circle are collinear.

A trigonometric proof in trilinear coordinates could be found at Prof. Campos' site. He credits Montes Valderrama (2004) with the discovery of the fact.

Michel Cabart came up with a generalization and a simple proof in barycentric coordinates.

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Copyright © 1996-2018 Alexander Bogomolny


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