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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.

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A Russian Telegram channel with over 700,000 followers is spreading disinformation about Russia's invasion of Ukraine under the guise of providing "objective information" and fact-checking fake news. Its influence extends beyond the platform, with major Russian publications, government officials, and journalists citing the page's posts. Emerson Brooking, a disinformation expert at the Atlantic Council's Digital Forensic Research Lab, said: "Back in the Wild West period of content moderation, like 2014 or 2015, maybe they could have gotten away with it, but it stands in marked contrast with how other companies run themselves today." "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. DFR Lab sent the image through Microsoft Azure's Face Verification program and found that it was "highly unlikely" that the person in the second photo was the same as the first woman. The fact-checker Logically AI also found the claim to be false. The woman, Olena Kurilo, was also captured in a video after the airstrike and shown to have the injuries. The gold standard of encryption, known as end-to-end encryption, where only the sender and person who receives the message are able to see it, is available on Telegram only when the Secret Chat function is enabled. Voice and video calls are also completely encrypted.
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