Let ABC be a triangle with (O),(I) being the circumcircle, and incircle respectively. Let (I) touch BC,CA, and AB at A0,B0,C0 let BC,CA, and AB intersect B0C0,C0A0,A0Bv at A1,B1, and C1 respectively. Prove that OI passes through the orthocenter of four triangles A0B0C0,A0B1C1,B0C1A1,C0A1B1.Nguyễn Minh Hà orthocentergeometrycollinearcircumcircleincircle