The apparent center of the Moon in the image is marked on the example image below. Note that although it seems off-center from the center of the visible portion of the Moon, it is the exact center with respect to the entire Moon's face, the invisible portion included.

The Moon's radius in pixels can easily be found by taking any of the three points you originally chose along the Moon's limb and using the following formula:

r = { (x_i - x_c)² + (y_i - y_c)² }^1/2      where i = 1, 2 or 3.

You should obtain the following value, regardless of the point(s) you chose:

r = 857.1317642 pixels.