For a triangle which two points of concurrence could be located outside the triangle

The incentre of a triangle is the intersection of all the angle bisectors of the triangle. It is always located inside the triangle.

The centroid of a triangle is the intersection of the lines joining the midpoint of each side of the triangle with the opposite vertex. I always lies within the triangle.

The orthocenter of a triangle is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. The othorcenter of the triangle does not alway lie inside the triangle.

The circumcenter of a triangle is the point where the perpendicular bisectors of a triangle intersect. The circumcenter is also the center of the triangle's circumcircle - the circle that passes through all three of the triangle's vertices. The circumcentre of a triangle is not always located inside the triangle.

Therefore, for a triangle, the two points of concurrence which could be located outside the triangle are the othorcenter and the circumcenter.