First, when X= 1, aq?bc, y is the smallest, and d is excluded.

After that, because it is obviously not a linear function, A is excluded.

When Q is at point C and Y is the largest, that is, X=3, we can get AQ= root 7 by using A as BC vertical line, trigonometric function and Pythagorean theorem.

So the maximum value is about 1.3, which is half of the root 7, excluding B.

So choose C.

Note: I am one of the candidates, and the process is written by myself. Please forgive me if the letters are written wrong.