Just started playing with geometric constructions and I was trying to find the center of a circle. I now know the bisect the chord then bisect the bisect method (https://www.mathsisfun.com/geometry/construct-circlecenter.html) but my first attempt involved using the compass to find the diameter of the circle by picking an arbitrary point increasing the size of the compass until it was as wide as it could be while still being within the circle. Using this method I then had the diameter which could be used a myriad of ways to find the center of the circle. So is this method valid? Can you use the compass to find the diameter of a circle in one step as I did or is this an invalid or valid method?
No, this is not allowed in the classical "straightedge-and-compass" constructions. The classical "collapsing" compasses can only draw a circle with a given centre and a given point on the circle. The "modern" compasses can use a radius that is the distance between any two given points. But in any case, you can't just "eyeball" the radius.