Let ABCD be a parallelogram. A line through C crosses the side AB at an interior point X,
and the line AD at Y. The tangents of the circle AXY at X and Y, respectively, cross at T.
Prove that the circumcircles of triangles ABD and TXY intersect at two points, one lying on the line AT and the other one lying on the line CT. RMM ShortlistgeometryAngle Chasing