Hello, R3ap3r!

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?

. . Butallof them have these four centers.

Circumcenter: the common intersection of the threeperpendicularbisectorsof the sides.

It is equidistant from the three vertices and hence is the center

. . of the circumscribing circle.

Incenter: the common intersection the threeanglebisectorsof 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 threemediansof 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 threealtitudesof the triangle.

(An altitude is drawn from a vertexperpendicularto the opposite side.)