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YGO 2024, 8 клас, Задача 2.

Нехай 𝐼 та 𝑂 — центри вписаного та описаного кіл трикутника 𝐴𝐵𝐶. Точки 𝑃 та 𝑄 такі, що 𝐴𝐼𝑂𝑃 та 𝐵𝐼𝑂𝑄 — рівнобічні трапеції (𝐴𝐼||𝑂𝑃, 𝐵𝐼||𝑂𝑄). Доведіть, що 𝐶𝑃 = 𝐶𝑄.

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YGO 2024, 8 клас, Задача 2.

Нехай 𝐼 та 𝑂 — центри вписаного та описаного кіл трикутника 𝐴𝐵𝐶. Точки 𝑃 та 𝑄 такі, що 𝐴𝐼𝑂𝑃 та 𝐵𝐼𝑂𝑄 — рівнобічні трапеції (𝐴𝐼||𝑂𝑃, 𝐵𝐼||𝑂𝑄). Доведіть, що 𝐶𝑃 = 𝐶𝑄.

Володимир Брайман

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On February 27th, Durov posted that Channels were becoming a source of unverified information and that the company lacks the ability to check on their veracity. He urged users to be mistrustful of the things shared on Channels, and initially threatened to block the feature in the countries involved for the length of the war, saying that he didn’t want Telegram to be used to aggravate conflict or incite ethnic hatred. He did, however, walk back this plan when it became clear that they had also become a vital communications tool for Ukrainian officials and citizens to help coordinate their resistance and evacuations. Apparently upbeat developments in Russia's discussions with Ukraine helped at least temporarily send investors back into risk assets. Russian President Vladimir Putin said during a meeting with his Belarusian counterpart Alexander Lukashenko that there were "certain positive developments" occurring in the talks with Ukraine, according to a transcript of their meeting. Putin added that discussions were happening "almost on a daily basis." To that end, when files are actively downloading, a new icon now appears in the Search bar that users can tap to view and manage downloads, pause and resume all downloads or just individual items, and select one to increase its priority or view it in a chat. 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%. "He has to start being more proactive and to find a real solution to this situation, not stay in standby without interfering. It's a very irresponsible position from the owner of Telegram," she said.
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