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На стороне BC треугольника ABC с ортоцентром H отмечена точка M. Перпендикуляр к BC в точке M пересекает прямые BH и CH в точках P и Q соответственно. Докажите, что ортоцентр треугольника HPQ лежит на прямой AM.

Мексиканская олимпиада 2024, Problem 4



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На стороне BC треугольника ABC с ортоцентром H отмечена точка M. Перпендикуляр к BC в точке M пересекает прямые BH и CH в точках P и Q соответственно. Докажите, что ортоцентр треугольника HPQ лежит на прямой AM.

Мексиканская олимпиада 2024, Problem 4

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