FULLANDPOINT Telegram 288
#геом_разминка

Задача. В треугольнике 𝐴𝐵𝐶, вписанном в окружность Ω, проведены высоты 𝐴𝐴₁ и 𝐶𝐶₁. Прямая 𝐴₁𝐶₁ пересекает Ω в точках 𝑃 и 𝑄. Точки 𝑃 ′ и 𝑄′ симметричны точкам 𝑃 и 𝑄 относительно сторон 𝐴𝐵 и 𝐵𝐶. Докажите, что 𝑃 ′𝑄′ ‖ 𝐴𝐶.



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#геом_разминка

Задача. В треугольнике 𝐴𝐵𝐶, вписанном в окружность Ω, проведены высоты 𝐴𝐴₁ и 𝐶𝐶₁. Прямая 𝐴₁𝐶₁ пересекает Ω в точках 𝑃 и 𝑄. Точки 𝑃 ′ и 𝑄′ симметричны точкам 𝑃 и 𝑄 относительно сторон 𝐴𝐵 и 𝐵𝐶. Докажите, что 𝑃 ′𝑄′ ‖ 𝐴𝐶.

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