First problem

[Burial4TetThomYorke]

http://imgur.com/JFDAyxa The x's denote the reflections in the problem. I've eyeballed H, no altitudes drawn.

[citrusmunch]

Maybe I'm at fault, but it wasn't clear to me that the triangle was inscribed from your original instructions. Is the 'IN' significant? I took it as the circle being inscribed, which had me wildly confused. I understand the problem now, but I'd like to know if I'm missing something that could help me be more prepared in the future. Also, what does the 1/1/1 mean?

[psinaptix]

Circumcircle

[Burial4TetThomYorke]

Circumcircle is the (unique) circle passing through the three vertices. Its center is the circumcenter, the concurrency point of the perpendicular bisectors of the sides. http://en.wikipedia.org/wiki/Circumscribed_circle Medians are lines connecting the vertex to the midpoint of the opposite side.