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ATOC and BTOC have equal area, circumcenter, altitude

Source: 2020 Dürer Math Competition Finals E1. 1

November 29, 2020
geometryequal areaequal areas

Problem Statement

Let ABCABC be an acute triangle where AC>BCAC > BC. Let TT denote the foot of the altitude from vertex CC, denote the circumcentre of the triangle by OO. Show that quadrilaterals ATOCATOC and BTOCBTOC have equal area.
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