
06282934
j
2014e.00580
Oai, Dao Thanh
A simple proof af Gibert's generalization of the Lester circle theorem.
Forum Geom. 14, 123125 (2014).
2014
Florida Atlantic University, Department of Mathematical Sciences, Boca Raton, FL
EN
G75
Lester circle theorem
rectangular hyperbola
http://forumgeom.fau.edu/FG2014volume14/FG201410index.html
The Lester circle theorem states that in any triangle, both Fermat points, the nine point center and the circumcenter lie on a circle. This admits a generalization given by Gilbert: every circle whose diameter is a cord of the Kiepert hyperbola perpendicular to the Euler line passes through the Fermat points. This paper gives a simple proof of this last statement based only on simple properties of rectangular hyperbolas.
Antonio M. Oller (Zaragoza)