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OI \perp AC, where I incenter and O circumcenter of excenters I_A,I_C, and I

Source: 2012 Oral Moscow Geometry Olympiad grades 8-9 p4

September 8, 2019
geometryincenterexcentersexcenterperpendicularcircumcircle

Problem Statement

In triangle ABCABC, point II is the center of the inscribed circle points, points IAI_A and ICI_C are the centers of the excircles, tangent to sides BCBC and ABAB, respectively. Point OO is the center of the circumscribed circle of triangle IIAICII_AI_C. Prove that OI⊥ACOI \perp AC
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