  The aim of this paper is to describe the largest inscribed circle into the
fundamental domains of a discontinuous group in Bolyai-Lobachevsky hyperbolic
plane. We give some known basic facts related to the Poincare-Delone problem
and the existence notion of the inscribed circle. We study the best circle of
the group G = [3, 3, 3, 3] with 4 rotational centers each of order 3. Using the
Lagrange multiplier method, we would describe the characteristic of the
best-inscribed circle. The method could be applied for the more general case in
G = [3, 3, 3,..., 3] with at least 4 rotational centers each of order 3, by
more and more computations. We observed by a more geometric Theorem 2 that the
maximum radius is attained by equalizing the angles at equivalent centers and
the additional vertices with trivial stabilizers, respectively. Theorem 3 will
close our arguments where Lemma 3 and 4 play key roles.
