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Triangles with Equal Areas

Source: APMO 2013, Problem 1

May 3, 2013
geometrytrigonometrycircumcircleparallelogramanalytic geometryequal areasratios

Problem Statement

Let ABCABC be an acute triangle with altitudes ADAD, BEBE, and CFCF, and let OO be the center of its circumcircle. Show that the segments OAOA, OFOF, OBOB, ODOD, OCOC, OEOE dissect the triangle ABCABC into three pairs of triangles that have equal areas.
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