In this problem it only states that there is a triangle and a pentagon inscribed into a circle.

I have a few questions for similar things showing up on the GRE:
It shows that they share a point at the top, but can we actually assume this? The answer assumes this, but if we were taking the actual GRE would this have to be stated to be true?
I believe that if the point is not shared we wouldn’t be able to tell the distance between the points and the answer would be indeterminant.

See this is where I am having an issue. There is no dot or label at the top point. I guess you can assume they are treating this is an intersection, but there is technically no intersection here.

Also just because distinct points are indeed distinct, the inverse does not have to be true.

This is obviously a bit pedantic, but can we assume that the question are in good faith, essentially that if two points look to be the same in the diagram they can be assumed to be the same?

I think uyou should go through pages 8 - 11 of the GRE Math Conventions that I shared
It would assuage the concerns you have and will let you know the things you can and can’t assume