Let ABC be a non-isosceles triangle. The incircle (I) of the triangle touches sides BC,CA,AB at A0,B0, and C0. Points A1,B1, and C1 are on BC,CA,AB such that BA1=CA0,CB1=AB0,AC1=BC0. Prove that the circumcircles (IAA1),(IBB1),(ICC1) pass all through a common point, distinct from I.Nguyễn Minh Hà geometrycircumcircleconcurrent circlesconcurrentincircleequal segments