A nice explanation of what you are trying to explain -- but subject to the restrictive definition of "outlier" that you use ("any point whose distance from the origin is more than some constant"). There is an alternate conception of "outlier" (as "a data point not consistent with the general pattern of the data") that is often more relevant to applications (e.g., for identifying possible measurement errors, data recording errors, or the presence of two or more sub-populations rather than a homogeneous population that can be described by a single nice distribution such a multivariate normal).