A Special Family of Triangles

Ivana Božić Dragun (), Helena Koncul () and Boris Odehnal ()
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Ivana Božić Dragun: Civil Engineering Department, Zagreb University of Applied Sciences, 10000 Zagreb, Croatia
Helena Koncul: Faculty of Civil Engineering, University of Zagreb, 10000 Zagreb, Croatia
Boris Odehnal: Institute of Art and Technology, University of Applied Arts Vienna, 1010 Vienna, Austria

Mathematics, 2025, vol. 13, issue 17, 1-15

Abstract: We study the one-parameter family of triangles that emerges if one sideline traces a pencil of lines and the opposite angle is fixed. A description of the traces of triangle centers and the pair of Brocard points in terms of parametrizations and equations is given. The envelopes of the families of circumcircles and nine-point circles are determined. Our approach even allows us to consider and treat the triangle family as a two-parameter family of triangles; i.e., the (interior) angle opposite to the pencil, which is in the beginning fixed, may also change.

Keywords: family of triangles; triangle centers; brocard points; quartic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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