NEUROGEOMETRY Telegram 62
Задача 41:
Автор - Ким Пётр

В треугольнике ABC точки X1, Y1 выбраны на стороне AB, X2, Y2 на стороне AC, а X3, Y3 на стороне BC таким образом, что X1Y2 параллелен X2Y1 параллелен BC, X3Y1 параллелен Y3X1 параллелен AC, X2Y3 параллелен Y2X3 параллелен AB.
Доказать, что середина отрезка между центрами (X1X2X3) и (Y1Y2Y3) лежит на прямой Эйлера треугольника ABC.
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Задача 41:
Автор - Ким Пётр

В треугольнике ABC точки X1, Y1 выбраны на стороне AB, X2, Y2 на стороне AC, а X3, Y3 на стороне BC таким образом, что X1Y2 параллелен X2Y1 параллелен BC, X3Y1 параллелен Y3X1 параллелен AC, X2Y3 параллелен Y2X3 параллелен AB.
Доказать, что середина отрезка между центрами (X1X2X3) и (Y1Y2Y3) лежит на прямой Эйлера треугольника ABC.

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