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Задача 58:
Автор - Роман Прозоров
Источник MGO 2024, задача 6

Внутри треугольника ABC отмечена точка P. Оказалось, что прямая, содержащая три внешних центра гомотетии пар вписанных в треугольники ABP, BCP, CPA окружности проходит через вершину ABC.
Доказать, что существует прямая, касающаяся окружностей, вписанных треугольники ABP, BCP, CPA.



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Задача 58:
Автор - Роман Прозоров
Источник MGO 2024, задача 6

Внутри треугольника ABC отмечена точка P. Оказалось, что прямая, содержащая три внешних центра гомотетии пар вписанных в треугольники ABP, BCP, CPA окружности проходит через вершину ABC.
Доказать, что существует прямая, касающаяся окружностей, вписанных треугольники ABP, BCP, CPA.

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