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Geometry Mathley 15.1 concurrent circumcircles, incircle related

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June 13, 2020
geometrycircumcircleconcurrent circlesconcurrentincircleequal segments

Problem Statement

Let ABCABC be a non-isosceles triangle. The incircle (I)(I) of the triangle touches sides BC,CA,ABBC,CA,AB at A0,B0A_0,B_0, and C0C_0. Points A1,B1A_1,B_1, and C1C_1 are on BC,CA,ABBC,CA,AB such that BA1=CA0,CB1=AB0,AC1=BC0BA1 = CA_0, CB_1 = AB_0, AC_1 = BC_0. Prove that the circumcircles (IAA1),(IBB1),(ICC1)(IAA1), (IBB_1), (ICC_1) pass all through a common point, distinct from II.
Nguyễn Minh Hà
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