id: 06282934
dt: j
an: 2014e.00580
au: Oai, Dao Thanh
ti: A simple proof af Gibertâ€™s generalization of the Lester circle theorem.
so: Forum Geom. 14, 123-125 (2014).
py: 2014
pu: Florida Atlantic University, Department of Mathematical Sciences, Boca
Raton, FL
la: EN
cc: G75
ut: Lester circle theorem; rectangular hyperbola
ci:
li: http://forumgeom.fau.edu/FG2014volume14/FG201410index.html
ab: 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.
rv: Antonio M. Oller (Zaragoza)