Let ABC be a triangle with incenter I and circumcircle Γ. Circles ωB passing through B and ωC passing through C are tangent at I. Let ωB meet minor arc AB of Γ at P and AB at M=B, and let ωC meet minor arc AC of Γ at Q and AC at N=C. Rays PM and QN meet at X. Let Y be a point such that YB is tangent to ωB and YC is tangent to ωC. Show that A,X,Y are collinear. geometryincentercircumcircleIMO ShortlistIMO Shortlist 2020tangentcollinear