Well, I guess there is a little bit confusion in terminology.
I'm not sure about what the "diameter" stands here for and do not want to be a smartass. So if I'm wrong, please correct me.
Two point of views, two different meanings;
1- If it is a simple geometry, you can not measure a diameter over the surface. Of course it must be measured in the same plane as the circumference.
In this regard, Greg T, you are 100% correct. And, king of the mill, I must respectfully disagree with you here. It is not an arc, it is direct line through the ball, extending from one side of the track to the other.
2- Diameter may stand for a unique meaning for the particular explanation which king of the mill has stated. Then in this case "diameter" holds a meaning other than basic geometry. If this is the case Greg T will be wrong and I will owe king of the mill an apology
Just my 2 cents..
Burak