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YGO 2024, 10-11 класи, Задача 2.

Нехай 𝑂 та 𝐻 — центр описаного кола та ортоцентр гострокутного трикутника 𝐴𝐵𝐶. На сторонах 𝐴𝐶 та 𝐴𝐵 відмітили точки 𝐷 та 𝐸 відповідно так, що відрізок 𝐷𝐸 проходить через точку 𝑂 та 𝐷𝐸||𝐵𝐶. На стороні 𝐵𝐶 обрали точки 𝑋 та 𝑌 такі, що 𝐵𝑋 = 𝑂𝐷 та 𝐶𝑌 = 𝑂𝐸. Доведіть, що ∠𝑋𝐻𝑌 + 2∠𝐵𝐴𝐶 = 180°.

Матвій Курський



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YGO 2024, 10-11 класи, Задача 2.

Нехай 𝑂 та 𝐻 — центр описаного кола та ортоцентр гострокутного трикутника 𝐴𝐵𝐶. На сторонах 𝐴𝐶 та 𝐴𝐵 відмітили точки 𝐷 та 𝐸 відповідно так, що відрізок 𝐷𝐸 проходить через точку 𝑂 та 𝐷𝐸||𝐵𝐶. На стороні 𝐵𝐶 обрали точки 𝑋 та 𝑌 такі, що 𝐵𝑋 = 𝑂𝐷 та 𝐶𝑌 = 𝑂𝐸. Доведіть, що ∠𝑋𝐻𝑌 + 2∠𝐵𝐴𝐶 = 180°.

Матвій Курський

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