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YGO 2024, 10-11 класи, Задача 1.

Нехай 𝐼 та 𝑂 — центри вписаного та описаного кіл прямокутного трикутника 𝐴𝐵𝐶 (∠𝐶 = 90°), 𝐾 — точка дотику вписаного кола з 𝐴𝐶, а 𝑃 та 𝑄 — точки перетину описаного кола трикутника 𝐴𝑂𝐾 з 𝑂𝐶 та з описаним колом трикутника 𝐴𝐵𝐶 відповідно. Доведіть, що точки 𝐶, 𝐼, 𝑃 та 𝑄 лежать на одному колі.

Михайло Сидоренко



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YGO 2024, 10-11 класи, Задача 1.

Нехай 𝐼 та 𝑂 — центри вписаного та описаного кіл прямокутного трикутника 𝐴𝐵𝐶 (∠𝐶 = 90°), 𝐾 — точка дотику вписаного кола з 𝐴𝐶, а 𝑃 та 𝑄 — точки перетину описаного кола трикутника 𝐴𝑂𝐾 з 𝑂𝐶 та з описаним колом трикутника 𝐴𝐵𝐶 відповідно. Доведіть, що точки 𝐶, 𝐼, 𝑃 та 𝑄 лежать на одному колі.

Михайло Сидоренко

BY Geometry Ukraine




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