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2020 IGO Intermediate P3

Source: 7th Iranian Geometry Olympiad (Intermediate) P3

November 4, 2020
geometrycircumcircleorthocenterIGO

Problem Statement

In acute-angled triangle ABCABC (AC>ABAC > AB), point HH is the orthocenter and point MM is the midpoint of the segment BCBC. The median AMAM intersects the circumcircle of triangle ABCABC at XX. The line CHCH intersects the perpendicular bisector of BCBC at EE and the circumcircle of the triangle ABCABC again at FF. Point JJ lies on circle ω\omega, passing through X,E,X, E, and FF, such that BCHJBCHJ is a trapezoid (CB∥HJCB \parallel HJ). Prove that JBJB and EMEM meet on ω\omega.
Proposed by Alireza Dadgarnia
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