  We consider a search algorithm for the output distribution that achieves the
channel capacity of a discrete memoryless channel. We will propose an algorithm
by iterated projections of an output distribution onto affine subspaces in the
set of output distributions. The problem of channel capacity has a similar
geometric structure as that of smallest enclosing circle for a finite number of
points in the Euclidean space. The metric in the Euclidean space is the
Euclidean distance and the metric in the space of output distributions is the
Kullback-Leibler divergence. We consider these two problems based on Amari's
$\alpha$-geometry. Then, we first consider the smallest enclosing circle in the
Euclidean space and develop an algorithm to find the center of the smallest
enclosing circle. Based on the investigation, we will apply the obtained
algorithm to the problem of channel capacity.
