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Geometry Mathley 9.1 4 collinear orthocenters

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June 7, 2020
orthocentergeometrycollinearcircumcircleincircle

Problem Statement

Let ABCABC be a triangle with (O),(I)(O), (I) being the circumcircle, and incircle respectively. Let (I)(I) touch BC,CABC,CA, and ABAB at A0,B0,C0A_0, B_0, C_0 let BC,CABC,CA, and ABAB intersect B0C0,C0A0,A0BvB_0C_0, C_0A_0, A_0Bv at A1,B1A_1, B_1, and C1C_1 respectively. Prove that OIOI passes through the orthocenter of four triangles A0B0C0,A0B1C1,B0C1A1,C0A1B1A_0B_0C_0, A_0B_1C_1, B_0C_1A_1,C_0A_1B_1.
Nguyễn Minh Hà
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