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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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The next bit isn’t clear, but Durov reportedly claimed that his resignation, dated March 21st, was an April Fools’ prank. TechCrunch implies that it was a matter of principle, but it’s hard to be clear on the wheres, whos and whys. Similarly, on April 17th, the Moscow Times quoted Durov as saying that he quit the company after being pressured to reveal account details about Ukrainians protesting the then-president Viktor Yanukovych. Telegram was founded in 2013 by two Russian brothers, Nikolai and Pavel Durov. Artem Kliuchnikov and his family fled Ukraine just days before the Russian invasion. Friday’s performance was part of a larger shift. For the week, the Dow, S&P 500 and Nasdaq fell 2%, 2.9%, and 3.5%, respectively. "We as Ukrainians believe that the truth is on our side, whether it's truth that you're proclaiming about the war and everything else, why would you want to hide it?," he said.
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