On some Curves Related to Pencil of Triangles in Isotropic Plane (CROSBI ID 665350)
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Podaci o odgovornosti
Katić Žlepalo, Mirela ; Jurkin, Ema
engleski
On some Curves Related to Pencil of Triangles in Isotropic Plane
We observe a pencil of triangles in isotropic plane whose vertices A and B are fixed, while vertex $C$ moves on the circumscribed circle. We prove that the locus of all centroids of triangles in such a pencil is a circle, the locus of all Gergonne points is a curve of order 4 and the locus of all symmedian centers is an ellipse. For the tangential triangles of all the triangles in such a pencil we prove that the locus of all centroids of all triangles is a line, the locus of all Gergonne points is an ellipse and the locus of all symmedian centers is a curve of order 3.
isotropic plane, pencil of triangles
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nije evidentirano
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nije evidentirano
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Podaci o prilogu
19-19.
2018.
objavljeno
Podaci o matičnoj publikaciji
Podaci o skupu
4. hrvatska konferencija za geometriju i grafiku
predavanje
02.09.2018-06.09.2018
Peroj, Hrvatska