Завершился кубок Колмогорова личной олимпиадой 🥇Публикуем ее условия 📝
Задача. Трапеция 𝐴𝐵𝐶𝐷 с основаниями 𝐴𝐷 и 𝐵𝐶 вписана в окружность 𝜔. Диагонали трапеции пересекаются в точке 𝐾. На лучах 𝐾𝐴 и 𝐾𝐵 выбраны точки 𝑋 и 𝑌 соответственно так, что отрезок 𝑋𝑌 касается 𝜔 в своей середине 𝑍. Докажите, что 𝑍 лежит на продолжении средней линии трапеции 𝐴𝐵𝐶𝐷.
Завершился кубок Колмогорова личной олимпиадой 🥇Публикуем ее условия 📝
Задача. Трапеция 𝐴𝐵𝐶𝐷 с основаниями 𝐴𝐷 и 𝐵𝐶 вписана в окружность 𝜔. Диагонали трапеции пересекаются в точке 𝐾. На лучах 𝐾𝐴 и 𝐾𝐵 выбраны точки 𝑋 и 𝑌 соответственно так, что отрезок 𝑋𝑌 касается 𝜔 в своей середине 𝑍. Докажите, что 𝑍 лежит на продолжении средней линии трапеции 𝐴𝐵𝐶𝐷.
These administrators had built substantial positions in these scrips prior to the circulation of recommendations and offloaded their positions subsequent to rise in price of these scrips, making significant profits at the expense of unsuspecting investors, Sebi noted. The S&P 500 fell 1.3% to 4,204.36, and the Dow Jones Industrial Average was down 0.7% to 32,943.33. The Dow posted a fifth straight weekly loss — its longest losing streak since 2019. The Nasdaq Composite tumbled 2.2% to 12,843.81. Though all three indexes opened in the green, stocks took a turn after a new report showed U.S. consumer sentiment deteriorated more than expected in early March as consumers' inflation expectations soared to the highest since 1981. A Russian Telegram channel with over 700,000 followers is spreading disinformation about Russia's invasion of Ukraine under the guise of providing "objective information" and fact-checking fake news. Its influence extends beyond the platform, with major Russian publications, government officials, and journalists citing the page's posts. The regulator took order for the search and seizure operation from Judge Purushottam B Jadhav, Sebi Special Judge / Additional Sessions Judge. That hurt tech stocks. For the past few weeks, the 10-year yield has traded between 1.72% and 2%, as traders moved into the bond for safety when Russia headlines were ugly—and out of it when headlines improved. Now, the yield is touching its pandemic-era high. If the yield breaks above that level, that could signal that it’s on a sustainable path higher. Higher long-dated bond yields make future profits less valuable—and many tech companies are valued on the basis of profits forecast for many years in the future.
from kr
