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IGO - Hard level - Problem 3

Source:

September 3, 2015
IGOgeometry

Problem Statement

let H H the orthocenter of the triangle ABC ABC
pass two lines l1 l_1 and l2 l_2 through H H such that l1⊥l2 l_1 \bot l_2
we have l1∩BC=D l_1 \cap BC = D and l1∩AB=Z l_1 \cap AB = Z
also l2∩BC=E l_2 \cap BC = E and l2∩AC=X l_2 \cap AC = X like this picture
pass a line d1 d_1 through D D parallel to AC AC and another line d2 d_2 through E E parallel to AB AB
let d1∩d2=Y d_1 \cap d_2 = Y
prove X X , , Y Y and Z Z are on a same line
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