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#геом_разминка

Задача. Пусть 𝑀 – середина диагонали 𝐴𝐶 равнобокой трапеции с основаниями 𝐵𝐶 и 𝐴𝐷 (𝐴𝐷 > 𝐵𝐶). Окружности Ω и 𝜔 описаны около треугольников 𝐴𝑀𝐷 и 𝐵𝑀𝐶 соответственно. Касательные к окружности 𝜔, проведённые в точках 𝐵 и 𝑀 пересекаются в точке 𝑃 . Докажите, что прямая 𝑃𝐴 касается окружности Ω.

С наступающим Новым годом 🎄☃️ Пусть у вас будут самые красивые ёлочные игрушки 🎄🔴
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#геом_разминка

Задача. Пусть 𝑀 – середина диагонали 𝐴𝐶 равнобокой трапеции с основаниями 𝐵𝐶 и 𝐴𝐷 (𝐴𝐷 > 𝐵𝐶). Окружности Ω и 𝜔 описаны около треугольников 𝐴𝑀𝐷 и 𝐵𝑀𝐶 соответственно. Касательные к окружности 𝜔, проведённые в точках 𝐵 и 𝑀 пересекаются в точке 𝑃 . Докажите, что прямая 𝑃𝐴 касается окружности Ω.

С наступающим Новым годом 🎄☃️ Пусть у вас будут самые красивые ёлочные игрушки 🎄🔴

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One thing that Telegram now offers to all users is the ability to “disappear” messages or set remote deletion deadlines. That enables users to have much more control over how long people can access what you’re sending them. Given that Russian law enforcement officials are reportedly (via Insider) stopping people in the street and demanding to read their text messages, this could be vital to protect individuals from reprisals. But Kliuchnikov, the Ukranian now in France, said he will use Signal or WhatsApp for sensitive conversations, but questions around privacy on Telegram do not give him pause when it comes to sharing information about the war. "There are a lot of things that Telegram could have been doing this whole time. And they know exactly what they are and they've chosen not to do them. That's why I don't trust them," she said. Ukrainian forces successfully attacked Russian vehicles in the capital city of Kyiv thanks to a public tip made through the encrypted messaging app Telegram, Ukraine's top law-enforcement agency said on Tuesday. Two days after Russia invaded Ukraine, an account on the Telegram messaging platform posing as President Volodymyr Zelenskiy urged his armed forces to surrender.
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