No matter how I move vertex C to create different triangles, the incircle always remains inside the triangle- hence [u]IN[/u]circle

As you can see, here is an instance of a triangle where the orthocenter lies outside the triangle

Point G is the centroid and no matter how I move a vertex to change the triangle, the centroid always remains inside the triangle

As you can see in this instance, the circumcenter lies outside the triangle