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#колм #красота_спасет_мир

Завершился кубок Колмогорова личной олимпиадой 🥇Публикуем ее условия 📝

Задача. Трапеция 𝐴𝐵𝐶𝐷 с основаниями 𝐴𝐷 и 𝐵𝐶 вписана в окружность 𝜔. Диагонали трапеции пересекаются в точке 𝐾. На лучах 𝐾𝐴 и 𝐾𝐵 выбраны точки 𝑋 и 𝑌 соответственно так, что отрезок 𝑋𝑌 касается 𝜔 в своей середине 𝑍. Докажите, что 𝑍 лежит на продолжении средней линии трапеции 𝐴𝐵𝐶𝐷.
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#колм #красота_спасет_мир

Завершился кубок Колмогорова личной олимпиадой 🥇Публикуем ее условия 📝

Задача. Трапеция 𝐴𝐵𝐶𝐷 с основаниями 𝐴𝐷 и 𝐵𝐶 вписана в окружность 𝜔. Диагонали трапеции пересекаются в точке 𝐾. На лучах 𝐾𝐴 и 𝐾𝐵 выбраны точки 𝑋 и 𝑌 соответственно так, что отрезок 𝑋𝑌 касается 𝜔 в своей середине 𝑍. Докажите, что 𝑍 лежит на продолжении средней линии трапеции 𝐴𝐵𝐶𝐷.

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Elsewhere, version 8.6 of Telegram integrates the in-app camera option into the gallery, while a new navigation bar gives quick access to photos, files, location sharing, and more. "He has kind of an old-school cyber-libertarian world view where technology is there to set you free," Maréchal said. After fleeing Russia, the brothers founded Telegram as a way to communicate outside the Kremlin's orbit. They now run it from Dubai, and Pavel Durov says it has more than 500 million monthly active users. Since January 2022, the SC has received a total of 47 complaints and enquiries on illegal investment schemes promoted through Telegram. These fraudulent schemes offer non-existent investment opportunities, promising very attractive and risk-free returns within a short span of time. They commonly offer unrealistic returns of as high as 1,000% within 24 hours or even within a few hours. Telegram, which does little policing of its content, has also became a hub for Russian propaganda and misinformation. Many pro-Kremlin channels have become popular, alongside accounts of journalists and other independent observers.
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