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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.



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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.

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"Russians are really disconnected from the reality of what happening to their country," Andrey said. "So Telegram has become essential for understanding what's going on to the Russian-speaking world." In 2014, Pavel Durov fled the country after allies of the Kremlin took control of the social networking site most know just as VK. Russia's intelligence agency had asked Durov to turn over the data of anti-Kremlin protesters. Durov refused to do so. Channels are not fully encrypted, end-to-end. All communications on a Telegram channel can be seen by anyone on the channel and are also visible to Telegram. Telegram may be asked by a government to hand over the communications from a channel. Telegram has a history of standing up to Russian government requests for data, but how comfortable you are relying on that history to predict future behavior is up to you. Because Telegram has this data, it may also be stolen by hackers or leaked by an internal employee. Also in the latest update is the ability for users to create a unique @username from the Settings page, providing others with an easy way to contact them via Search or their t.me/username link without sharing their phone number. False news often spreads via public groups, or chats, with potentially fatal effects.
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