In a scalene triangle ABC, the points E and F are the foot of altitudes drawn from B and C, respectively. The points X and Y are the reflections of the vertices B and C to the line EF, respectively. Let the circumcircles of the △ABC and △AEF intersect at T for the second time. Show that the four points A,X,Y,T lie on a single circle. geometryAZE JUNIOR NATIONAL MOAZE SENIOR NATIONAL MO