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Через центр O описанной окружности треугольника ABC проведена прямая, пересекающая стороны AB, BC и CA в точках F, D и E соответственно. Докажите, что окружности, построенные на AD, BE и CF как на диаметрах пересекаются в двух точках, одна из которых лежит на описанной окружности треугольника ABC, а вторая на окружности девяти точек.



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Через центр O описанной окружности треугольника ABC проведена прямая, пересекающая стороны AB, BC и CA в точках F, D и E соответственно. Докажите, что окружности, построенные на AD, BE и CF как на диаметрах пересекаются в двух точках, одна из которых лежит на описанной окружности треугольника ABC, а вторая на окружности девяти точек.

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In 2018, Russia banned Telegram although it reversed the prohibition two years later. Recently, Durav wrote on his Telegram channel that users' right to privacy, in light of the war in Ukraine, is "sacred, now more than ever." Oleksandra Matviichuk, a Kyiv-based lawyer and head of the Center for Civil Liberties, called Durov’s position "very weak," and urged concrete improvements. "For Telegram, accountability has always been a problem, which is why it was so popular even before the full-scale war with far-right extremists and terrorists from all over the world," she told AFP from her safe house outside the Ukrainian capital. The account, "War on Fakes," was created on February 24, the same day Russian President Vladimir Putin announced a "special military operation" and troops began invading Ukraine. The page is rife with disinformation, according to The Atlantic Council's Digital Forensic Research Lab, which studies digital extremism and published a report examining the channel.
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