When you do a collision test, GD does a fast bounding circle check before the real collision algorithm (SAT) to discard some objects. This means that if you use the distance check yourself as a collision test it will be faster than the GD collision test (because the SAT algorithm won’t be used at all). And if you use the squared distance you’ll get an even faster collision test (because sqrt() is slow).
To check the squared distance:
Where the variable radius of A is the radius of the bounding circle that you want to use as circle shape for A (from the Center point, if you want to use a different center you’ll have to calculate the distance yourself), the same for B. Take into account that if you use a circle-circle collision test, very wide or very hight things like lasers will have a very bad response
The sources says that the distance condition uses the center point, but I haven’t tried it.
EDIT: I confirm that the centre point is used for sprites, and (X + Width/2, Y + Height/2) (center) is used for the other objects:
