Let ABC be an acute-angled triangle whose inscribed circles

Let ABC be an acute-angled triangle whose inscribed circles touches AB and AC at D and E respectively. Let X and Y be the points of intersection of the bisectors of the angles sudut AC B and sudut ABC with the line D E and let Z be the midpoint of BC . Prove that the triangle X Y Z is equilateral if and only if sudut A=60 .