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Київська міська олімпіада 2025, 2 тур, 9.4

Нехай 𝐻 – точка перетину висот, а точка 𝑂 – центр описаного кола трикутника 𝐴𝐵𝐶. Пряма 𝐴𝐻 вдруге перетинає описане коло ∆𝐴𝐵𝐶 в точці 𝑁. Описане коло ∆𝐵𝑂𝐶 з центром в точці 𝑄 вдруге перетинає пряму 𝑂𝐻 в точці 𝑋. Доведіть, що точки 𝑂,𝑄, 𝑁, 𝑋 лежать на одному колі.

Матвій Курський



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Київська міська олімпіада 2025, 2 тур, 9.4

Нехай 𝐻 – точка перетину висот, а точка 𝑂 – центр описаного кола трикутника 𝐴𝐵𝐶. Пряма 𝐴𝐻 вдруге перетинає описане коло ∆𝐴𝐵𝐶 в точці 𝑁. Описане коло ∆𝐵𝑂𝐶 з центром в точці 𝑄 вдруге перетинає пряму 𝑂𝐻 в точці 𝑋. Доведіть, що точки 𝑂,𝑄, 𝑁, 𝑋 лежать на одному колі.

Матвій Курський

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