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The Bevan Point: Triangle, Circumcircle, Excentral Triangle, Circumcenter, Excenter, Perpendicular, Concurrency. Level: High School, College. Step-by-step illustration. HTML5 Animation for iPad and Nexus

The Bevan point V of a triangle ABC is the circumcenter V of the excentral triangle DEF. Also, V is the point of concurrence of the perpendiculars from the excenters to the respective sides.

Benjamin Bevan, an English civil engineer proposed this theorem in the Proceedings of the Edinburgh Mathematical Society: Leybourn's Mathematical Repository, new series, I. 18 (pagination of the Questions to be answered).

The proof of Bevan's theorem given in the Mathematical Repository Vol. I., Part I., p. 143, is by John Butterworth of Haggate.

 

Bevan Point Triangle
 


 

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