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YGO 2024, 9 клас, Задача 2.

Нехай 𝑀 — середина сторони 𝐵𝐶 трикутника 𝐴𝐵𝐶, 𝐷 — довільна точка на дузі 𝐵𝐶 описаного кола, яка не містить точку 𝐴, 𝑁 — середина 𝐴𝐷. Коло, яке проходить через точки 𝐴, 𝑁 і дотикається до 𝐴𝐵, перетинає сторону 𝐴𝐶 у точці 𝐸. Доведіть, шо точки 𝐶, 𝐷, 𝐸 та 𝑀 лежать на одному колі.

Матвій Курський



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YGO 2024, 9 клас, Задача 2.

Нехай 𝑀 — середина сторони 𝐵𝐶 трикутника 𝐴𝐵𝐶, 𝐷 — довільна точка на дузі 𝐵𝐶 описаного кола, яка не містить точку 𝐴, 𝑁 — середина 𝐴𝐷. Коло, яке проходить через точки 𝐴, 𝑁 і дотикається до 𝐴𝐵, перетинає сторону 𝐴𝐶 у точці 𝐸. Доведіть, шо точки 𝐶, 𝐷, 𝐸 та 𝑀 лежать на одному колі.

Матвій Курський

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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." Telegram boasts 500 million users, who share information individually and in groups in relative security. But Telegram's use as a one-way broadcast channel — which followers can join but not reply to — means content from inauthentic accounts can easily reach large, captive and eager audiences. The Security Service of Ukraine said in a tweet that it was able to effectively target Russian convoys near Kyiv because of messages sent to an official Telegram bot account called "STOP Russian War." In a statement, the regulator said the search and seizure operation was carried out against seven individuals and one corporate entity at multiple locations in Ahmedabad and Bhavnagar in Gujarat, Neemuch in Madhya Pradesh, Delhi, and Mumbai. Some people used the platform to organize ahead of the storming of the U.S. Capitol in January 2021, and last month Senator Mark Warner sent a letter to Durov urging him to curb Russian information operations on Telegram.
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