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.

Two points D and E are defined using geometric constructions:
D is the intersection of the angle bisectors;
E is the center of the circumcircle (circle through the points A, B, C).

Exploration 1: Notice that points A, B, C are described as "Free Points" so you can
click and drag them wherever you'd like. Play around with that.

Exploration 2: What other objects can you click and drag?

Questions 1: Can you move the triangle corners so that
1) E lies outside the triangle?
2) D lies outside the triangle?
3) What is your conjecture?

Questions 2: Can you move the triangle corners so that
1) E lies inside the triangle DBC?
2) E lies inside the triangle DAB?
3) E lies on the line a?
4) How would you describe the shape is the triangle ABC each of these cases?

Question 3:
1) Can you move the line segment b so that D and E coincide?
2) How would you describe the shape of the triangle in that case?

Volker Ecke, Created with GeoGebra