Triangle: angle bisectors, circumcircle, etc...

The picture below shows a triangle ABC. Move one of the points A, B, or C to change the shape of the triangle.

Now, four points D, E, I and J are defined using geometric constructions.

Exploration 1: How do these four points move as you change the triangle?

Question 1: Which of those is the centroid, the incenter, the orthoccenter,
and the circumcenter? How do you know for sure?

Informal Writing Task #1:
Based on your explorations, informally state several (i.e. at least five)
conjectures that explain ways in which the
1) Centroid, circumcenter, incenter, and orthocenter depend on the
geometry of the triangle, and,
2) Centroid, circumcenter, incenter, and orthocenter are related to each other.

Exploration 2: Can you change the triangle so that all four points D, E, I, and J coincide?

Question #3: If you can get all four points to coincide, how would you
describe the shape of the triangle ABC in that situation?

Volker Ecke, Created with GeoGebra