I was wondering if someone could show me how to do prove these in a Euclidean way:
I need to show that the following three statements are equivalent for the triangle ABC,
gamma (the angle opposite AB) = 90 degrees
C is the orthocenter of ABC
the midpoint of AB is the circumcenter of ABC
I think I can prove this if I show the first implies the second, the second implies the third, and the third implies the first. I drew out diagrams and I see that it makes sense, but I'm having trouble writing it out in a more rigorous way.
Any help would be appreciated. Thanks in advance.