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Подошел к концу третий день турнира Колмогорова, и мы, как обычно, радуем вас задачами с него 💥
Задача. На сторонах 𝐵𝐶, 𝐶𝐴 и 𝐴𝐵 треугольника 𝐴𝐵𝐶 выбраны точки 𝐴₁, 𝐵₁ и 𝐶₁ соответственно. Четырёхугольники 𝐴𝐵₁𝐴₁𝐶₁, 𝐵𝐶₁𝐵₁𝐴₁ и 𝐶𝐴₁𝐶₁𝐵₁ описаны около окружностей с центрами 𝐼𝑎, 𝐼𝑏 и 𝐼𝑐 соответственно. Докажите, что площади треугольников 𝐴₁𝐵₁𝐶₁ и 𝐼𝑎𝐼𝑏𝐼𝑐 отличаются в четыре раза.
Подошел к концу третий день турнира Колмогорова, и мы, как обычно, радуем вас задачами с него 💥
Задача. На сторонах 𝐵𝐶, 𝐶𝐴 и 𝐴𝐵 треугольника 𝐴𝐵𝐶 выбраны точки 𝐴₁, 𝐵₁ и 𝐶₁ соответственно. Четырёхугольники 𝐴𝐵₁𝐴₁𝐶₁, 𝐵𝐶₁𝐵₁𝐴₁ и 𝐶𝐴₁𝐶₁𝐵₁ описаны около окружностей с центрами 𝐼𝑎, 𝐼𝑏 и 𝐼𝑐 соответственно. Докажите, что площади треугольников 𝐴₁𝐵₁𝐶₁ и 𝐼𝑎𝐼𝑏𝐼𝑐 отличаются в четыре раза.
Pavel Durov, Telegram's CEO, is known as "the Russian Mark Zuckerberg," for co-founding VKontakte, which is Russian for "in touch," a Facebook imitator that became the country's most popular social networking site. The channel appears to be part of the broader information war that has developed following Russia's invasion of Ukraine. The Kremlin has paid Russian TikTok influencers to push propaganda, according to a Vice News investigation, while ProPublica found that fake Russian fact check videos had been viewed over a million times on Telegram. Crude oil prices edged higher after tumbling on Thursday, when U.S. West Texas intermediate slid back below $110 per barrel after topping as much as $130 a barrel in recent sessions. Still, gas prices at the pump rose to fresh highs. In the United States, Telegram's lower public profile has helped it mostly avoid high level scrutiny from Congress, but it has not gone unnoticed. The War on Fakes channel has repeatedly attempted to push conspiracies that footage from Ukraine is somehow being falsified. One post on the channel from February 24 claimed without evidence that a widely viewed photo of a Ukrainian woman injured in an airstrike in the city of Chuhuiv was doctored and that the woman was seen in a different photo days later without injuries. The post, which has over 600,000 views, also baselessly claimed that the woman's blood was actually makeup or grape juice.
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