calculate thew center of a circle passing through the following 3 points

That is, get the position with equal distance from three given points

p1: lon (-90 .. +90):
lat (-180..+180):
p2: lon (-90 .. +90)
lat (-180..+180):
p3: lon (-90 .. +90):
lat (-180..+180):

Note: No AI was used, just plain pen and paper algebra