J. García and Paul Yiu, Golden sections of triangle centers in the
Forum Geometricorum, 16 (2016) 119--124.
Abstract. A golden triangle is one whose vertices are among the vertices of a regular pentagon. There are two kinds of golden triangles, short and tall, which are isosceles triangles with vertical angles 108 degrees and 36 degrees respectively. We consider some basic triangle centers of a short and tall golden triangles sharing one vertex and with the same circumcircle, and exhibit pairs of basic triangle centers divided in the golden ratio by another triangle center.
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