
Journal for Geometry and Graphics 21 (2017), No. 1, 061070 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 [ Fulltextpdf (725 KB)] 