It takes a while to get them sorted in the brain . . .
Triangles have many shapes: equilateral, isosceles, acute, right, obtuse, etc.What exactly is the difference between circumcenter, incenter, centroid, and orthocenter?
. . But all of them have these four centers.
Circumcenter: the common intersection of the three perpendicular bisectors of the sides.
It is equidistant from the three vertices and hence is the center
. . of the circumscribing circle.
Incenter: the common intersection the three angle bisectors of the triangle.
It is equidistance from the three sides of the triangle
. . and is the center of iscribed circle.
Centroid: the common intersection of the three medians of the triangle.
(A median joins a vertex to the midpoint of the opposite side.)
This point is the center of gravity (mass) of the triangle.
Orthocenter: the common intersection of the three altitudes of the triangle.
(An altitude is drawn from a vertex perpendicular to the opposite side.)