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Acute triangle, equality of areas

Source: XIII Polish Junior MO 2018 Second Round - Problem 2

April 24, 2018
geometryareaPlane GeometryPolandquadrilateralcircumcircle

Problem Statement

Let ABCABC be an acute traingle with AC≠BCAC \neq BC. Point KK is a foot of altitude through vertex CC. Point OO is a circumcenter of ABCABC. Prove that areas of quadrilaterals AKOCAKOC and BKOCBKOC are equal.
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