engleski

Family of triangles and related curves

The article observes a one-parameter triangle family T. We prove that the sets of the orthocenters, centroids, circumcenters and the midpoints of the variable triangle side of the triangle family T lie on four different hyperbolae. Furthermore, there is constructed an envelope $k^4_3 of the perpendicular bisectors of the variable triangle sides. Also it is constructed a bicircular rational quartic as an envelope of the circumcircles of the triangle family T.

triangle centers ; family of triangles ; envelope of lines ; envelope of circles

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