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B', A', O are collinear

Source: European Mathematical Cup, 2015, Junior, P4

December 30, 2016
geometry

Problem Statement

Let ABCABC be an acute angled triangle. Let B′,A′B' , A' be points on the perpendicular bisectors of AC,BCAC, BC respectively such that B′A⊥ABB'A \perp AB and A′B⊥ABA'B \perp AB. Let PP be a point on the segment ABAB and OO the circumcenter of the triangle ABCABC. Let D,ED, E be points on BC,ACBC, AC respectively such that DP⊥BODP \perp BO and EP⊥AOEP \perp AO. Let O′O' be the circumcenter of the triangle CDECDE. Prove that B′,A′B', A' and O′O' are collinear.
Steve Dinh
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