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Задача 56:
Автор - Григорий Забазнов
Источник: MGO 2024, задача 4

На сторонах AB и AC треугольника ABC выбраны точки E и F соответственно так,что B,E,F,C лежат на одной окружности. Прямые BF и CE пересекаются в точке K. Отражение прямой AK относительно биссетрисы угла BAC пересекает BF и CE в точках M и N.
Доказать, что если окружность (MKN) касается BC, то она касается и EF.



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Задача 56:
Автор - Григорий Забазнов
Источник: MGO 2024, задача 4

На сторонах AB и AC треугольника ABC выбраны точки E и F соответственно так,что B,E,F,C лежат на одной окружности. Прямые BF и CE пересекаются в точке K. Отражение прямой AK относительно биссетрисы угла BAC пересекает BF и CE в точках M и N.
Доказать, что если окружность (MKN) касается BC, то она касается и EF.

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