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#геом_разминка

Задача. Пусть 𝐼 — центр вписанной окружности остроугольного треугольника 𝐴𝐵𝐶. Точки 𝑃, 𝑄, 𝑅 выбраны на сторонах 𝐴𝐵, 𝐵𝐶, 𝐶𝐴 соответственно так, что 𝐴𝑃 = 𝐴𝑅 и 𝐵𝑃 = 𝐵𝑄, и ∠𝑃𝐼𝑄 =∠𝐵𝐴𝐶. Докажите, что 𝑄𝑅 ⊥ 𝐴𝐶.

В международный день гор, желаем вам достигнуть новых высот 🪜



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#геом_разминка

Задача. Пусть 𝐼 — центр вписанной окружности остроугольного треугольника 𝐴𝐵𝐶. Точки 𝑃, 𝑄, 𝑅 выбраны на сторонах 𝐴𝐵, 𝐵𝐶, 𝐶𝐴 соответственно так, что 𝐴𝑃 = 𝐴𝑅 и 𝐵𝑃 = 𝐵𝑄, и ∠𝑃𝐼𝑄 =∠𝐵𝐴𝐶. Докажите, что 𝑄𝑅 ⊥ 𝐴𝐶.

В международный день гор, желаем вам достигнуть новых высот 🪜

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