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IMOC 2018 G5 (IX//OH, incenter, circumcenter, orthocenter, euler line)

Source: https://artofproblemsolving.com/community/c6h1740825p11314688

March 22, 2020
geometryincenterCircumcenterorthocenterparallelEuler Line

Problem Statement

Suppose I,O,HI,O,H are incenter, circumcenter, orthocenter of △ABC\vartriangle ABC respectively. Let D=AI∩BCD = AI \cap BC,E=BI∩CAE = BI \cap CA, F=CI∩ABF = CI \cap AB and XX be the orthocenter of △DEF\vartriangle DEF. Prove that IX∥OHIX \parallel OH.
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