Centroid can lie outside the triangle.
False
Centroid is the point of intersection of the medians of a triangle. Median is a line segment drawn from a vertex of a triangle in such a way a way that it divides the side opposite to the vertex in two equal parts. Since, medians can only intersect inside the triangle irrespective of the triangle, so the centroid always lies inside the triangle.
Thus, the given statement is false.