let us consider following problem:
we have inscribed triangle,like this
we are asked to determine if given $x$ is acute or obtuse,$O$ is center of circle,as i know if $CB$ would be diameter,then $x$ would be $90$,or $CAB$ would be right triangle,but in this case what it should be?if i trust diagram then maybe it seems that it is more then $90$,but because GRE said that dont trust diagram,then what i should know about it?
There is a proposition that says that if you connect $C$ to $O$ and $B$ to $O$, then the reflex $\angle BOC$ is twice of $\angle BAC$. And since reflex $\angle BOC >180^{\circ}$, we are done.
To argue that the reflex $\angle BOC >180^{\circ}$, we can just say that the usual $\angle BOC <180^{\circ}$, because it is contained in the triangle $BOC$.
See: http://www.mathopenref.com/arccentralangletheorem.html (The prop will be a corollary of that.)