Сегодня на кубке Колмогорова 🏆 прошли вторые туры матбоев. Присоединяйтесь к обсуждению матчей и задач в комментариях👇
Задача. Точки 𝐻 и 𝑂 – ортоцентр и центр описанной окружности остроугольного неравнобедренного треугольника 𝐴𝐵𝐶 соответственно. Точки 𝑃 и 𝑄 выбраны на описанной окружности 𝜔 так, что ∠𝐵𝑃𝐻 = ∠𝐶𝑄𝐻 = 90°. Пусть прямая 𝑃𝑄 пересекает касательную к 𝜔, проведенную в точке 𝐴, в точке 𝑆, а отрезки 𝑂𝑃 и 𝑂𝑄 пересекают отрезки 𝐵𝐻 и 𝐶𝐻 в точках 𝑋 и 𝑌 соответственно. Докажите, что 𝑂𝑆 ‖ 𝑋𝑌.
Сегодня на кубке Колмогорова 🏆 прошли вторые туры матбоев. Присоединяйтесь к обсуждению матчей и задач в комментариях👇
Задача. Точки 𝐻 и 𝑂 – ортоцентр и центр описанной окружности остроугольного неравнобедренного треугольника 𝐴𝐵𝐶 соответственно. Точки 𝑃 и 𝑄 выбраны на описанной окружности 𝜔 так, что ∠𝐵𝑃𝐻 = ∠𝐶𝑄𝐻 = 90°. Пусть прямая 𝑃𝑄 пересекает касательную к 𝜔, проведенную в точке 𝐴, в точке 𝑆, а отрезки 𝑂𝑃 и 𝑂𝑄 пересекают отрезки 𝐵𝐻 и 𝐶𝐻 в точках 𝑋 и 𝑌 соответственно. Докажите, что 𝑂𝑆 ‖ 𝑋𝑌.
The regulator took order for the search and seizure operation from Judge Purushottam B Jadhav, Sebi Special Judge / Additional Sessions Judge. The regulator said it has been undertaking several campaigns to educate the investors to be vigilant while taking investment decisions based on stock tips. On February 27th, Durov posted that Channels were becoming a source of unverified information and that the company lacks the ability to check on their veracity. He urged users to be mistrustful of the things shared on Channels, and initially threatened to block the feature in the countries involved for the length of the war, saying that he didn’t want Telegram to be used to aggravate conflict or incite ethnic hatred. He did, however, walk back this plan when it became clear that they had also become a vital communications tool for Ukrainian officials and citizens to help coordinate their resistance and evacuations. Telegram has become more interventionist over time, and has steadily increased its efforts to shut down these accounts. But this has also meant that the company has also engaged with lawmakers more generally, although it maintains that it doesn’t do so willingly. For instance, in September 2021, Telegram reportedly blocked a chat bot in support of (Putin critic) Alexei Navalny during Russia’s most recent parliamentary elections. Pavel Durov was quoted at the time saying that the company was obliged to follow a “legitimate” law of the land. He added that as Apple and Google both follow the law, to violate it would give both platforms a reason to boot the messenger from its stores. Investors took profits on Friday while they could ahead of the weekend, explained Tom Essaye, founder of Sevens Report Research. Saturday and Sunday could easily bring unfortunate news on the war front—and traders would rather be able to sell any recent winnings at Friday’s earlier prices than wait for a potentially lower price at Monday’s open.
from ar
