The Triangle problem

A triangle $ABC$ has incenter $I$ . Points $X$ and $Y$ are located on the line segment $AB$ and $AC$ , respectively so that $BX\cdot AB = IB^2$ and $CY \cdot AC = IC^2$ . Given that $X,Y$ and $I$ are collinear, find the possible value of the measure of angle $A$ in degrees.