1. Consider a 2-D data set, in which two categories of data are included. These two categories of data are points sampled in two circles with same radius and intersecting at a point. As shown in the following figure, the black and solid dots denote the sampled points; B point is the point of intersection of two circles; A and C points are two sampled points farthest away from each other in two circles. Except B point, the distance between each point in the left circle and C point is larger than that between it and A; the distance between each point in the right circle and C point is less than that between it and A. The distance between B and A is same as that between B and C.

Now you are required to use k-means clustering method to cluster the above data points into two groups. The different initial means could incur different clustering results of k-means. If we adopt B and C as initial means and A and C as initial means, what clustering results can be obtained, respectively? Please answer the question and explain the reason briefly. [10 points]