Originally Posted by

**PvtBillPilgrim** 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,

(1) gamma (the angle opposite AB) = 90 degrees

(2) C is the orthocenter of ABC

(3) 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.