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English

# the points of tangency between the johnson circles and the anticomplementary circle form another triangle, called the anticomplementary triangle of the reference triangle.

Russian

# Точки касания окружностей Джонсона и антикомплементарной окружности образуют треугольник, носящий название "антикомплементарный треугольник" опорного треугольника.

Last Update: 2016-03-03
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English

applied to the anticomplementary triangle, which is itself obtained from the johnson triangle by a homothety with factor 2, it follows from composition of homotheties that the reference triangle is homothetic to the johnson triangle by a factor −1.

Russian

Применяя это свойство к антикомплементарному треугольнику, который сам получается из треугольника Джонсона гомотетией с множителем 2, из композиции гомотетий получим, что опорный треугольник подобен треугольнику Джонсона с множителем −1.

Last Update: 2016-03-03
Usage Frequency: 1
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English

trilinear coordinates for the vertices of the anticomplementary triangle, x'y'z', are given by* x' = −1/a : 1/b : 1/c* y' = 1/a : −1/b : 1/c* z' = 1/a : 1/b : −1/cthe name "anticomplementary triangle" corresponds to the fact that its vertices are the anticomplements of the vertices a, b, c of the reference triangle.

Russian

Трилинейные координаты вершин антикомплементарного треугольника x'y'z' задаются формулами* x' = −1/a : 1/b : 1/c* y' = 1/a : −1/b : 1/c* z' = 1/a : 1/b : −1/c

Last Update: 2016-03-03
Usage Frequency: 1
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