A Cat(0) metric space $(X,d)$ is approximately flat if there exists a dense subset $U\subset X$ such that every $x\in U$ has a flat neighborhood.

I'm interested in a generalization of Radon's theorem (https://matthewhr.wordpress.com/2013/02/27/radons-theorem/) to approximately flat Cat(0) spaces. Do you know if there exists one?

Thank you.