MathDB
SL 2015 G1: Prove that IJ=AH

Source: IMO 2015 Shortlist, G1

July 7, 2016
geometryIMO ShortlistTriangle

Problem Statement

Let ABCABC be an acute triangle with orthocenter HH. Let GG be the point such that the quadrilateral ABGHABGH is a parallelogram. Let II be the point on the line GHGH such that ACAC bisects HIHI. Suppose that the line ACAC intersects the circumcircle of the triangle GCIGCI at CC and JJ. Prove that IJ=AHIJ = AH.
Back to ProblemsView on AoPS