Points Of Concurrency in Triangles

Author:
knwilson
Points of Concurrency in Triangles
What are the centroid, the incenter, the circumcenter, and the orthocenter of a triangle? How do the points of concurrency in triangles help solve problems? Does the centroid always lie inside the triangle? Does the incenter always lie inside the triangle? Does the circumcenter always lie inside the triangle? Does the orthocenter always lie inside the triangle? Can these points ever coincide?