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CD _|_ EO if AB=AC, O circumcenter, AD=//DB. E centroid ACD

Source: 2017 Ecuador Juniors (OMEC) L2 p3

October 25, 2022
geometryperpendicularisosceles

Problem Statement

Given an isosceles triangle ABCABC with AB=ACAB = AC. Let OO be the circumcenter of ABCABC, DD the midpoint of ABAB and EE the centroid of ACDACD. Prove that CD⊥EOCD \perp EO.
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