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YGO 2024, 9 клас, Задача 5.

Нехай 𝐴𝐿 — бісектриса трикутника 𝐴𝐵𝐶, 𝑂 — центр кола, описано го навколо цього трикутника, 𝐷 та 𝐸 — середини 𝐵𝐿 та 𝐶𝐿 відповідно. На відрізках 𝐴𝐷 та 𝐴𝐸 відмітили точки 𝑃 та 𝑄 так, що 𝐴𝑃𝐿𝑄 паралелограм. Доведіть, що 𝑃𝑄 ⟂ 𝐴𝑂.

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YGO 2024, 9 клас, Задача 5.

Нехай 𝐴𝐿 — бісектриса трикутника 𝐴𝐵𝐶, 𝑂 — центр кола, описано го навколо цього трикутника, 𝐷 та 𝐸 — середини 𝐵𝐿 та 𝐶𝐿 відповідно. На відрізках 𝐴𝐷 та 𝐴𝐸 відмітили точки 𝑃 та 𝑄 так, що 𝐴𝑃𝐿𝑄 паралелограм. Доведіть, що 𝑃𝑄 ⟂ 𝐴𝑂.

Михайло Плотніков

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He floated the idea of restricting the use of Telegram in Ukraine and Russia, a suggestion that was met with fierce opposition from users. Shortly after, Durov backed off the idea. "And that set off kind of a battle royale for control of the platform that Durov eventually lost," said Nathalie Maréchal of the Washington advocacy group Ranking Digital Rights. "There are a lot of things that Telegram could have been doing this whole time. And they know exactly what they are and they've chosen not to do them. That's why I don't trust them," she said. 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. The news also helped traders look past another report showing decades-high inflation and shake off some of the volatility from recent sessions. The Bureau of Labor Statistics' February Consumer Price Index (CPI) this week showed another surge in prices even before Russia escalated its attacks in Ukraine. The headline CPI — soaring 7.9% over last year — underscored the sticky inflationary pressures reverberating across the U.S. economy, with everything from groceries to rents and airline fares getting more expensive for everyday consumers.
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