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A simple proof af Gibert’s generalization of the Lester circle theorem. (English)
Forum Geom. 14, 123-125 (2014).
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.
Reviewer: Antonio M. Oller (Zaragoza)
Classification: G75
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