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Задача. Высоты 𝐵𝐵₁ и 𝐶𝐶₁ остроугольного треугольника 𝐴𝐵𝐶 пересекаются в точке 𝐻. Пусть 𝐵₂ и 𝐶₂ — точки на отрезках 𝐵𝐻 и 𝐶𝐻 соответственно такие, что 𝐵𝐵₂ = 𝐵₁𝐻 и 𝐶𝐶₂ = 𝐶₁𝐻. Описанная окружность треугольника 𝐵₂𝐻𝐶₂ пересекает описанную окружность треугольника 𝐴𝐵𝐶 в точках 𝐷 и 𝐸. Докажите, что треугольник 𝐷𝐸𝐻 прямоугольный.
Задача. Высоты 𝐵𝐵₁ и 𝐶𝐶₁ остроугольного треугольника 𝐴𝐵𝐶 пересекаются в точке 𝐻. Пусть 𝐵₂ и 𝐶₂ — точки на отрезках 𝐵𝐻 и 𝐶𝐻 соответственно такие, что 𝐵𝐵₂ = 𝐵₁𝐻 и 𝐶𝐶₂ = 𝐶₁𝐻. Описанная окружность треугольника 𝐵₂𝐻𝐶₂ пересекает описанную окружность треугольника 𝐴𝐵𝐶 в точках 𝐷 и 𝐸. Докажите, что треугольник 𝐷𝐸𝐻 прямоугольный.
The picture was mixed overseas. Hong Kong’s Hang Seng Index fell 1.6%, under pressure from U.S. regulatory scrutiny on New York-listed Chinese companies. Stocks were more buoyant in Europe, where Frankfurt’s DAX surged 1.4%. 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. Just days after Russia invaded Ukraine, Durov wrote that Telegram was "increasingly becoming a source of unverified information," and he worried about the app being used to "incite ethnic hatred." "Like the bombing of the maternity ward in Mariupol," he said, "Even before it hits the news, you see the videos on the Telegram channels." "The argument from Telegram is, 'You should trust us because we tell you that we're trustworthy,'" Maréchal said. "It's really in the eye of the beholder whether that's something you want to buy into."
from hk
