В треугольнике ABC (AB<AC) точка O — центр описанной окружности. Серединный перпендикуляр к BC пересекает прямые BC, CA и AB в точках D, E и F. Окружности с диаметрами EF и AO пересекаются в точках X и Y. Докажите, что окружности (XYD) и (ABC) касаются.
В треугольнике ABC (AB<AC) точка O — центр описанной окружности. Серединный перпендикуляр к BC пересекает прямые BC, CA и AB в точках D, E и F. Окружности с диаметрами EF и AO пересекаются в точках X и Y. Докажите, что окружности (XYD) и (ABC) касаются.
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