Musselman's theorem (original) (raw)
В евклидовой геометрии теорема Массельмана — это свойство некоторых окружностей, определённых для произвольного треугольника.
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| dbo:abstract | In Euclidean geometry, Musselman's theorem is a property of certain circles defined by an arbitrary triangle. Specifically, let be a triangle, and , , and its vertices. Let , , and be the vertices of the , obtained by mirroring each vertex of across the opposite side. Let be the circumcenter of . Consider the three circles , , and defined by the points , , and , respectively. The theorem says that these three Musselman circles meet in a point , that is the inverse with respect to the circumcenter of of the isogonal conjugate or the nine-point center of . The common point is point in Clark Kimberling's list of triangle centers. (en) В евклидовой геометрии теорема Массельмана — это свойство некоторых окружностей, определённых для произвольного треугольника. (ru) В евклідовій геометрії теорема Масельмана — це властивість деяких кіл, визначених для довільного трикутника. (uk) |
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| rdfs:comment | В евклидовой геометрии теорема Массельмана — это свойство некоторых окружностей, определённых для произвольного треугольника. (ru) В евклідовій геометрії теорема Масельмана — це властивість деяких кіл, визначених для довільного трикутника. (uk) In Euclidean geometry, Musselman's theorem is a property of certain circles defined by an arbitrary triangle. Specifically, let be a triangle, and , , and its vertices. Let , , and be the vertices of the , obtained by mirroring each vertex of across the opposite side. Let be the circumcenter of . Consider the three circles , , and defined by the points , , and , respectively. The theorem says that these three Musselman circles meet in a point , that is the inverse with respect to the circumcenter of of the isogonal conjugate or the nine-point center of . (en) |
| rdfs:label | Musselman's theorem (en) Теорема Массельмана (ru) Теорема Масельмана (uk) |
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