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Окружности ω1 и ω2 пересекаются в точках X и Y, лежат внутри окружности Ω и касаются её в точках A и B. Прямая AB повторно пересекает окружности ω1 и ω2 в точках C и D соответственно. Вписанная в криволинейный треугольник CDX окружность касается стороны CD в точке Z. Докажите, что XZ — биссектриса угла AXB.



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#геометрия #задача

Окружности ω1 и ω2 пересекаются в точках X и Y, лежат внутри окружности Ω и касаются её в точках A и B. Прямая AB повторно пересекает окружности ω1 и ω2 в точках C и D соответственно. Вписанная в криволинейный треугольник CDX окружность касается стороны CD в точке Z. Докажите, что XZ — биссектриса угла AXB.

BY JustScience | Олимпиадная Математика




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He adds: "Telegram has become my primary news source." Messages are not fully encrypted by default. That means the company could, in theory, access the content of the messages, or be forced to hand over the data at the request of a government. Artem Kliuchnikov and his family fled Ukraine just days before the Russian invasion. But Telegram says people want to keep their chat history when they get a new phone, and they like having a data backup that will sync their chats across multiple devices. And that is why they let people choose whether they want their messages to be encrypted or not. When not turned on, though, chats are stored on Telegram's services, which are scattered throughout the world. But it has "disclosed 0 bytes of user data to third parties, including governments," Telegram states on its website. "He has to start being more proactive and to find a real solution to this situation, not stay in standby without interfering. It's a very irresponsible position from the owner of Telegram," she said.
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