Let k be incircle of acute triangle ABC, AC=BC, and l be excircle that touches AB. Line p through the C is orthogonal to AB, p∩k={X,Y} , p∩l={Z,T} and the point arrangement is X−Y−Z−T. Circle m through X and Z intersects AB at D and E. Prove that points D,Y,E,T are concyclic. geometrySerbian competition