#6. I looked at the original triangle I had created with the original centroid, orthocenter, circumcenter, and incenter. Then I constructed a medial triangle by connecting the midpoints of all three sides of the original triangle. In this medial triangle, I constructed the centriod, orthocenter, circumcenter, and incenter in itself. What I noticed was that the centroid was the same as the centroid in the original triangle. What was interesting was that the incenter of the medial triangle was now where the centroid (of the original and medial) was. Also, the orthocenter of the medial triangle is where the circumcenter of the original triangle was, and the circumcenter of the medial triangle is where the incenter of the original triangle was. I checked this three times to make sure that the information I found was correct.

#12. Unfortunately, my web site was down so I looked up concurrent in the Webster Dictionary. It said concurrent meant that things happened at the same time, so I interpreted that to mean that I was to prove that the perpendicular bisectors occur at the same point. So I constructed the perpendicular bisectors of all the sides of the triangle. They all intersected at the same point. I assume that this proves that they occur at the same point.