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4 collinear orhocenters wanted, incenter of tangential ABCD related

Source: 2013 Thailand October Camp Geometry Exam p3

October 22, 2020
geometryincentercollinearorthocentertangential

Problem Statement

Let OO be the incenter of a tangential quadrilateral ABCDABCD. Prove that the orthocenters of △AOB\vartriangle AOB, △BOC\vartriangle BOC, △COD\vartriangle COD, △DOA\vartriangle DOA lie on a line.
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