Geometry Question.?

Question

Which of the following can fall outside of a triangle? Centroid, Incenter, Orthocenter, and Circumcenter. Which ones?

Answer 1

Orthocenter and circumcenter.

The centroid is the point of intersection of the medians. Medians never extend outside the triangle, so neither can their intersection.

The incenter is the point of intersection of the angle bisectors. Angle bisectors never extend outside of the triangle, so neither can their intersection.

The orthocenter is the point of intersection of the altitudes. Two altitudes of an obtuse triangle are completely outside of the triangle, so the point of intersection of the altitudes must also be outside of the triangle in such a case.

The circumcenter is the point of intersection of the perpendicular bisecors. In an obtuse triangle, the circumcenter lies outside of the triangle.

Answer 2

INCENTER