Geodesic
On the Invariance of Brocard Angles in the Interior and Exterior Pappus Triangles of any Given Triangle
Journal for geometry and graphics, Tome 21 (2017) no. 1, pp. 61-7 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 51M04, 51M25
Mots-clés : Brocard angles, Brocard points, Brocard circle, Pappus triangles, Miquel points, symmedian point 
@article{JGG_2017_21_1_JGG_2017_21_1_a5,
     author = {V. Oxman and A. Sigler and M. Stupel },
     title = {On the {Invariance} of {Brocard} {Angles} in the {Interior} and {Exterior} {Pappus} {Triangles} of any {Given} {Triangle}},
     journal = {Journal for geometry and graphics},
     pages = {61--7},
     year = {2017},
     volume = {21},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2017_21_1_JGG_2017_21_1_a5/}
}
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V. Oxman; A. Sigler; M. Stupel . On the Invariance of Brocard Angles in the Interior and Exterior Pappus Triangles of any Given Triangle. Journal for geometry and graphics, Tome 21 (2017) no. 1, pp. 61-7. http://geodesic.mathdoc.fr/item/JGG_2017_21_1_JGG_2017_21_1_a5/