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IMOC 2019 G1 (DE pass through orthocenter of BIC, BD=CA,CE=BA, incenter)

Source: https://artofproblemsolving.com/community/c6h1958463p13536764

March 21, 2020
geometryorthocenterincenter

Problem Statement

Let II be the incenter of a scalene triangle △ABC\vartriangle ABC. In other words, AB‾,BC‾,CA‾\overline{AB},\overline{BC},\overline{CA} are distinct. Prove that if D,ED,E are two points on rays BA→,CA→\overrightarrow{BA},\overrightarrow{CA}, satisfying BD‾=CA‾,CE‾=BA‾\overline{BD}=\overline{CA},\overline{CE}=\overline{BA} then line DEDE pass through the orthocenter of △BIC\vartriangle BIC. http://2.bp.blogspot.com/-aHCD5tL0FuA/XnYM1LoZjWI/AAAAAAAALeE/C6hO9W9FGhcuUP3MQ9aD7SNq5q7g_cY9QCK4BGAYYCw/s1600/imoc2019g1.png
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