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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 515=17, 2013.

Izvorni znanstveni članak

Family of triangles and related curves

Ana Sliepčević ; Faculty of Civil Engineering, University of Zagreb, 10 000 Zagreb, Kačića 26, Croatia
Helena Halas orcid id orcid.org/0000-0002-6890-7835 ; Faculty of Civil Engineering, University of Zagreb, 10 000 Zagreb, Kačića 26, Croatia

Puni tekst: engleski pdf 831 Kb

str. 203-210

preuzimanja: 473

citiraj

Sažetak

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_3^4 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.

Ključne riječi

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

Hrčak ID:

104418

URI

https://hrcak.srce.hr/104418

Datum izdavanja:

27.6.2013.

Posjeta: 865 *