Let A B C D be a square with side length 1. Points X and Y are on sides B C and C D respectively such that the areas of triangles A B X, X C Y, and Y D A are equal. Find the ratio of the area of \triangle A X Y to the area of \triangle X C Y.
Let A B C D be a square with side length 1. Points X and Y are on sides B C and C D respectively such that the areas of triangles A B X, X C Y, and Y D A are equal. Find the ratio of the area of \triangle A X Y to the area of \triangle X C Y.