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perpendicularity if and only if AB=AC

Source: bmo 1985

April 23, 2007
geometrycircumcircleanalytic geometrygraphing linescomplex numbersgeometry proposed

Problem Statement

In a given triangle ABCABC, OO is its circumcenter, DD is the midpoint of ABAB and EE is the centroid of the triangle ACDACD. Show that the lines CDCD and OEOE are perpendicular if and only if AB=ACAB=AC.
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