Let triangle ABC be a given acute scalene triangle with altitudes BE and CF. Let D be the point where the incircle of △ABC touches side BC. The circumcircle of △BDE meets line AB again at point K, the circumcircle of △CDF meets line AC again at point L. The circumcircle of △BDE and △CDF meet line KL again at X and Y, respectively. Prove that the incenter of △DXY lies on the incircle of △ABC.Proposed by Luu Dong, Vietnam
geometryincenterAngle-chasing