Vladislav Natchev
American College of Sofia (Bulgaria)
https://doi.org/10.53656/math2025-4-1-gcs
Abstract. Under stereographic projection, the projection point is collinear with the Lemoine points of the projection and the projected triangles or with
the centers of their Apollonian circles (Natchev 2025). In the current paper, we generalize the discovered property of stereographic projection by proving
that it applies to every point on the plane expressed in the barycentric form (δa2 : εb2 : ρc2), where δ, ε, ρ ∈ R. For a particular case, we investigate the
points on the symmedians of the triangle and the tangents to the circumcircle at the vertices, where we derive collinearity of two more notable points of a triangle, namely the feet of the symmedians and the vertices of the tangential triangle. By setting the planimetric equivalent of the newly found facts, we connect the configurations they give rise to with Olympiad geometry.
Keywords: stereographic projection, collinearity, Olympiad geometry
Свързани статии:
Apollonian Sphere and Properties of Stereographic Projection around the Lemoine Point
Устойчивост на резултатите при повторно измерване с тест и отчитане на успеваемостта на учениците след проведена дидактическа технология
Сравнение на форматите на ДЗИ за профилирана подготовка по избрани матуритетни предмети и прогноза за очакваните резултати от тях
Заключителна кръгла маса по проект „Социални и педагогически аспекти на проблема за употребата на психоактивни вещества“
