Question

does a material always lie in the interior of the triangle

Answer 1

Let me break this down for you. A centroid is the point of concurrency for the 3 medians of a triangle, when the 3 medians are congruent. Therefore, the centroid of a triangle is always in the center of a triangle. Keep in mind that the centroid of a triangle is 2/3 the distance from the vertex to the midpoint of the opposite side.

Answer 2

The altitude of a triangle (in the sense it used here) is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. ... The orthocenter is not always inside the triangle. If the triangle is obtuse, it will be outside.