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On the Generalized Gergonne Point and Beyond (CROSBI ID 140823)

Prilog u časopisu | izvorni znanstveni rad

Hoffmann, Miklos ; Gorjanc, Sonja On the Generalized Gergonne Point and Beyond // Forum geometricorum, 8 (2008), 151-155

Podaci o odgovornosti

Hoffmann, Miklos ; Gorjanc, Sonja

engleski

On the Generalized Gergonne Point and Beyond

In this paper we generalize the concept of Gergonne point which is a well-known center of the triangle. Given a triangle $V_1V_2V_3$, a point $I$ and three arbitrary directions, we find a distance $x=IQ_1=IQ_2=IQ_3$ along these directions, for which the three cevians $V_iQ_i$ are concurrent. Types and number of solutions, which can be obtained by the common intersection points of three conics, are also discussed in detail.

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Podaci o izdanju

8

2008.

151-155

objavljeno

1534-1178

Povezanost rada

Matematika