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Prove that AO is parallel HK if IO is parallel to BC.

Source: ToT 2003 SA-4

July 3, 2011
geometrycircumcirclegeometric transformationparallelogramrectanglegeometry proposed

Problem Statement

In a triangle ABCABC, let HH be the point of intersection of altitudes, II the center of incircle, OO the center of circumcircle, KK the point where the incircle touches BCBC. Given that IOIO is parallel to BCBC, prove that AOAO is parallel to HKHK.
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