Circle Constructions

Relation between special lines and points in a triangle. The triangle's vertices can be dragged to form different triangles. Here are some questions that you can think about.... 1. How do we construct all these with compass and straight edge? (In particular, the incircle...) 2. The centroid (center of gravity) splits each median into a certain ratio. What is the ratio and why is it so? 3. Which of these centers can be outside of the triangle? When does that happen? 4. Which three of the centers are collinear? What is that line called and what is the length ratio split by those three points?