GAUSS8 2006 Problem 23

In the diagram, the points are evenly spaced vertically and horizontally. A segment AB is drawn using two of the points, as shown. Point C is chosen to be one of the remaining 18 points. For how many of these 18 possible points is triangle ABC isosceles?

Image

Answer Choices
A. 6
B. 4
C. 5
D. 2
E. 3