Centriod  Incenter
Orthocenter   all four points together
Angle bisector instructions     Perpendicular bisector instructions
Median instructions    Altitude instructions
Period 3     Period 4     Period 5
 

The circumcenter is the intersection of the perpendicular bisectors of a triangle.
To construct an perpendicular bisector refer to your textbook, page 39.
Remember, the two arc must be the same length.
It is a good idea to make them the length from the segment that is being bisected.
The circumcenter allows you to circumscribe a circle around a triangle.
To do this you would place your compass on the circumcenter,
with the radius the length from the circumcenter to on of the verticies of the triangle.