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#геом_разминка

Задача. В треугольнике 𝐴𝐵𝐶 проведена медиана 𝐵𝑀. На касательной в точке 𝐶 к описанной окружности треугольника 𝐵𝑀𝐶 отмечена точка 𝐷 так, что ∠𝐶𝐵𝐷 = 90°. Отрезки 𝐴𝐷 и 𝐵𝑀 пересекаются в точке 𝐸. Докажите, что центр описанной окружности треугольника 𝐵𝐷𝐸 лежит на прямой 𝐴𝐶.



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#геом_разминка

Задача. В треугольнике 𝐴𝐵𝐶 проведена медиана 𝐵𝑀. На касательной в точке 𝐶 к описанной окружности треугольника 𝐵𝑀𝐶 отмечена точка 𝐷 так, что ∠𝐶𝐵𝐷 = 90°. Отрезки 𝐴𝐷 и 𝐵𝑀 пересекаются в точке 𝐸. Докажите, что центр описанной окружности треугольника 𝐵𝐷𝐸 лежит на прямой 𝐴𝐶.

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