Kohonen networks. Why is the dot product used?

Question

Neural networks

I'm trying to deal with the question of training the Kohonen layer. After the implementation of the algorithm, a question arose. As written in the book, linear weighted adders are used as the neurons of the Kohonen network.

So, suppose we have several clusters on the XOY plane with centers at points A,
B, C.

If, when searching for the "winning neuron", we use the scalar product of the input vector data and the weight vector of each neuron, then in this case (after training) the winner will always be the neuron "responsible" for the cluster centered at point C, since the product of its weight vector with the input data vector will always be maximum (for the first quarter).
How then to distinguish between clusters centered at these points?