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Radical axis perpendicular to OI

Source: IMOC 2021 G5

August 11, 2021
geometryradical axistangential quadrilateralperpendicular

Problem Statement

The incircle of a cyclic quadrilateral ABCDABCD tangents the four sides at EE, FF, GG, HH in counterclockwise order. Let II be the incenter and OO be the circumcenter of ABCDABCD. Show that the line connecting the centers of ⊙(OEG)\odot(OEG) and ⊙(OFH)\odot(OFH) is perpendicular to OIOI.
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