CAYLEY 2014 Problem 25

Point P is on the $y-$axis with $y-$coordinate greater than 0 and less than 100. A circle is drawn through P,Q(4,4) and O(0,0). How many possible positions for P are there so that the radius of this circle is an integer?

Answer Choices
A. 2
B. 68
C. 66
D. 65
E. 67