INMO 1991 Problem 5

Triangle $ABC$ has an incenter $I$ . Let points $X$ , $Y$ be located on the line segments $AB$ , $AC$ respectively, so that $BX \cdot AB = IB^2$ and $CY \cdot AC = IC^2$ . Given that the points $X, I, Y$ lie on a straight line, find the possible values of the measure of angle $A$ .