Points of Concurrency in Triangles

1. What are the centroid, the incenter, the circumcenter, and the orthocenter of a triangle?[br][br]2. How do the points of concurrency in triangles help solve problems?[br][br]3. Does the centroid always lie inside the triangle?[br][br]4. Does the incenter always lie inside the triangle?[br][br]5. Does the circumcenter always lie inside the triangle?[br][br]6. Does the orthocenter always lie inside the triangle?[br][br]7. Can these points ever coincide?