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Points Of Concurrency in Triangles

Points of Concurrency in Triangles
What are the centroid, the incenter, the circumcenter, and the orthocenter of a triangle? How can the centroid 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 all be in one place?