Еще одна задача с колма. Без картинки. Дан вписанный пятиугольник P1P2P3P4P5; положим P6 = P1 и P0 = P5. При k = 1, 2, 3, 4, 5 обозначим через Ik центр вписанной окружности треугольника Pk−1PkPk+1. Оказалось, что пяти- угольник I1I2I3I4I5 также является вписанным. Докажите, что прямые P1I1, P2I2, P3I3, P4I4 и P5I5 пересекаются в одной точке.
Еще одна задача с колма. Без картинки. Дан вписанный пятиугольник P1P2P3P4P5; положим P6 = P1 и P0 = P5. При k = 1, 2, 3, 4, 5 обозначим через Ik центр вписанной окружности треугольника Pk−1PkPk+1. Оказалось, что пяти- угольник I1I2I3I4I5 также является вписанным. Докажите, что прямые P1I1, P2I2, P3I3, P4I4 и P5I5 пересекаются в одной точке.
BY Геометрия-канал
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