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Київська міська олімпіада 2025, 2 тур, 7.4

Нехай 𝐵𝐸 і 𝐶𝐹 − медіани △ 𝐴𝐵𝐶, 𝐺 − точка їх перетину. На відрізках 𝐺𝐹 та 𝐺𝐸 знайшлися точки 𝐾 і 𝐿 відповідно такі, що 𝐵𝐾=𝐶𝐿=𝐴𝐺. Доведіть, що ∠𝐵𝐾𝐹 +∠𝐶𝐿𝐸 =∠𝐵𝐺𝐶.

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Київська міська олімпіада 2025, 2 тур, 7.4

Нехай 𝐵𝐸 і 𝐶𝐹 − медіани △ 𝐴𝐵𝐶, 𝐺 − точка їх перетину. На відрізках 𝐺𝐹 та 𝐺𝐸 знайшлися точки 𝐾 і 𝐿 відповідно такі, що 𝐵𝐾=𝐶𝐿=𝐴𝐺. Доведіть, що ∠𝐵𝐾𝐹 +∠𝐶𝐿𝐸 =∠𝐵𝐺𝐶.

Вадим Соломка

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