Draw any line (a chord of the circumference) on the picture.
This line intersects the edge of the circumference on two points.
Measure (pixels units) the length of this line between these endpoints.
Divide it up into equal parts.
Now you can have the midpoint, M, find it helped by the programm SalsaJ.
Draw a perpendicular to the line through the midpoint.
Measure (on that line) the distance from M to the edge of the circunference of the Moon.
Using your knoledges related with circumference's properties, find out the Moon's diameter.