Let ABC be a scalene triangle with circumcircle Ω and incenter I. Ray AI meets BC at D and meets Ω again at M; the circle with diameter DM cuts Ω again at K. Lines MK and BC meet at S, and N is the midpoint of IS. The circumcircles of △KID and △MAN intersect at points L1 and L2. Prove that Ω passes through the midpoint of either IL1 or IL2.Proposed by Evan Chen USA(J)MOUSAMO2017 USAMOgeometryHi