Question

Answer each of the following questions and explain how you know.

1. Does the centroid always lie inside the triangle?

2. Does the incenter always lie inside the triangle?

3. Does the circumcenter always lie inside the triangle?

4. Does the orthocenter always lie inside the triangle?

5. Can these points ever coincide?

Answer 1

1. Yes
2. yes
3. no
4. no
5. Yes, only if it's an Equiangular triangles.