\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2014e.00580}
\itemau{Oai, Dao Thanh}
\itemti{A simple proof af Gibert's generalization of the Lester circle theorem.}
\itemso{Forum Geom. 14, 123-125 (2014).}
\itemab
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.
\itemrv{Antonio M. Oller (Zaragoza)}
\itemcc{G75}
\itemut{Lester circle theorem; rectangular hyperbola}
\itemli{http://forumgeom.fau.edu/FG2014volume14/FG201410index.html}
\end