Journal for Geometry and Graphics 21 (2017), No. 1, 061--070
Copyright Heldermann Verlag 2017
On the Invariance of Brocard Angles in the Interior and Exterior Pappus Triangles of any Given Triangle
Victor Oxman
Western Galilee College, P.O.B. 2125, Acre 24121, Israel
victor.oxman@gmail.com
Avi Sigler
Shaanan College, P.O.B. 906, Haifa 26109, Israel
anysig@walla.co.il
Moshe Stupel
Shaanan College, P.O.B. 906, Haifa 26109, Israel
stupel@bezeqint.net
The paper presents groups of triangles inscribed in a given triangle ABC that have the same Brocard angle as ABC. Some of them are similar to ABC and some are not. The central group consists of the exterior and interior Pappus triangles of ABC. We prove that the Miquel points of Pappus triangles produce pedal triangles that have the same Brocard angle as ABC. Furthermore, we prove that the locus of all points, that produce pedal triangles inside ABC with the same Brocard angle, is a circle. For Miquel points of exterior Pappus triangles, we prove that all these points are located on the Brocard circle.
Keywords: Brocard angles, Brocard points, Brocard circle, Pappus triangles, Miquel points, symmedian point.
MSC: 51M04; 51M25
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