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Задача 48:
Автор - Чуев Савва

Обобщение одного известного факта про точку Болтая...

Четырёхугольник ABCD вписан в окружность с центром O. E - точка пересечения его диагоналей, F - точка пересечения продолжений сторон AB и CD, Б - проекция Ο на EF. На сторонах AB и CD, как на основаниях, во внешнюю сторону построены подобные равнобедренные треугольники ABX и CDY. Докажите, что точки O, Б, X, Y лежат на одной окружности.



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Задача 48:
Автор - Чуев Савва

Обобщение одного известного факта про точку Болтая...

Четырёхугольник ABCD вписан в окружность с центром O. E - точка пересечения его диагоналей, F - точка пересечения продолжений сторон AB и CD, Б - проекция Ο на EF. На сторонах AB и CD, как на основаниях, во внешнюю сторону построены подобные равнобедренные треугольники ABX и CDY. Докажите, что точки O, Б, X, Y лежат на одной окружности.

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