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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.

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At this point, however, Durov had already been working on Telegram with his brother, and further planned a mobile-first social network with an explicit focus on anti-censorship. Later in April, he told TechCrunch that he had left Russia and had “no plans to go back,” saying that the nation was currently “incompatible with internet business at the moment.” He added later that he was looking for a country that matched his libertarian ideals to base his next startup. Emerson Brooking, a disinformation expert at the Atlantic Council's Digital Forensic Research Lab, said: "Back in the Wild West period of content moderation, like 2014 or 2015, maybe they could have gotten away with it, but it stands in marked contrast with how other companies run themselves today." 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. In view of this, the regulator has cautioned investors not to rely on such investment tips / advice received through social media platforms. It has also said investors should exercise utmost caution while taking investment decisions while dealing in the securities market. 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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