# Centroids, Orthocenters, Circumcenters, and Incenters

Now that we've located the centroid (G), orthocenter (H), circumcenter (C), and incenter (I), let's explore the relationships among them

First let's construct a line segment between points H and C

Here we notice that point G is a point on segment HC

When changing the shape of the triangle we notice that point G stayed in the center of the triangle and is still a point

on line segment HC

Again changing the shape of triangle ABC we notice that the circumcenter tends to move toward the midpoint of the side, where the orthocenter moves toward the vertex

Changing the shape a tad bit more we notice that the circumcenter does in fact exit the triangle via the midpoint and the orthocenter via the vertex. All along point G stayed on segment HC

The following sketches shows that the circumcenter always exits via the midpoint and the orthocenter via the vertex

And finally looking at the points throughout the sketches we can see how the circumcenter looks to always be equidistant from the vertexes and the incenter looks to always be equidistant from the sides of the triangle