Let ABC be an acute triangle and A1,B1,C1 be the touchpoints of the excircles with the segments BC,CA,AB respectively. Let OA,OB,OC be the circumcenters of △AB1C1,△BC1A1,△CA1B1 respectively. Prove that the lines through OA,OB,OC respectively parallel to the internal angle bisectors of ∠A,∠B,∠C are concurrent. geometrycircumcircleangle bisector