I fail to understand how the circled point is assigned to cluster c2 and not c1. From what I have understood, the points are assigned to the (nearest?) centroid in order to minimise the squared distances i.e. to minimise the assignment cost.
Visually too, it appears to me that the circled point belongs to the first cluster.
Please correct me if I'm wrong.
Source - http://www.cs.yale.edu/homes/el327/papers/OnlineKMeansAlenexEdoLiberty.pdf