Unsupervised anomaly detection: assigning the clusters to normal and anomaly
The radius depends on the number of clusers you choose. The more clusters, the smaller the radius.

If you have labelled data, you could eliminate the outliers/anomalies for determining the threshold radii for your clusters. For example you could take the greatest distance from the cluster center to its members (smaller radius for higher detection rate as stated in your question).

This question is closely related to the question Anomaly/outlier detection using fuzzy clustering. I am reposting my answer:

As far as I know there is no unique definition for what is an outlier/anomaly. Therefore you'll have to decide by yourself what the characteristics of outlying data points in your data set are. This could be for example: distance to the cluster center (threshold), local neighbourhood (a data point that has no/few data points in its neighgbourhood might be an outlier) or statistical characteristics (an outlier doesn't 'fit' to the distribution of a cluster, e.g. Grubbs' method). You can find a survey of outlier detection methods in A Survey of Outlier Detection Methodologies by Hodge and Austin (2004).