Problem

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Tags: IGO, geometry



let $ H $ the orthocenter of the triangle $ ABC $ pass two lines $ l_1 $ and $ l_2 $ through $ H $ such that $ l_1 \bot l_2 $ we have $ l_1 \cap BC = D $ and $ l_1 \cap AB = Z $ also $ l_2 \cap BC = E $ and $ l_2 \cap AC = X $ like this picture pass a line $ d_1$ through $ D $ parallel to $ AC $ and another line $ d_2 $ through $ E $ parallel to $ AB $ let $ d_1 \cap d_2 = Y $ prove $ X $ $ , $ $ Y $ and $ Z $ are on a same line


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