intersection between a circle and a great line segment

[Pomax]

Hiya, I found http://www.movable-type.co.uk/scripts/latlong.html while searching for help on how to calculate the intersection point(s) of a circle with radius R centered at some GPS coordinate C, and the great line segment between two arbitrary coordinates A and B, but didn't find anything on the page that really helped with that, how would one calculate those?