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.
Given the pro-privacy stance of the platform, it’s taken as a given that it’ll be used for a number of reasons, not all of them good. And Telegram has been attached to a fair few scandals related to terrorism, sexual exploitation and crime. Back in 2015, Vox described Telegram as “ISIS’ app of choice,” saying that the platform’s real use is the ability to use channels to distribute material to large groups at once. Telegram has acted to remove public channels affiliated with terrorism, but Pavel Durov reiterated that he had no business snooping on private conversations. Ukrainian forces have since put up a strong resistance to the Russian troops amid the war that has left hundreds of Ukrainian civilians, including children, dead, according to the United Nations. Ukrainian and international officials have accused Russia of targeting civilian populations with shelling and bombardments. At its heart, Telegram is little more than a messaging app like WhatsApp or Signal. But it also offers open channels that enable a single user, or a group of users, to communicate with large numbers in a method similar to a Twitter account. This has proven to be both a blessing and a curse for Telegram and its users, since these channels can be used for both good and ill. Right now, as Wired reports, the app is a key way for Ukrainians to receive updates from the government during the invasion. The Dow Jones Industrial Average fell 230 points, or 0.7%. Meanwhile, the S&P 500 and the Nasdaq Composite dropped 1.3% and 2.2%, respectively. All three indexes began the day with gains before selling off. False news often spreads via public groups, or chats, with potentially fatal effects.
from ms
