Let us consider a convex planar set E: among all the chords
bisecting the area, there is a minimal one. An old problem (presented also
in the book "Unsolved problems in Geometry", 1991, and known as "Santalo'
problem") is the following: if we fix this minimal length, which set has the
smallest possible area? It is reasonable to guess that this set must be the
ball, but thanks to the work of Zindler (1921) it is known that it is not
so. In particular, Zindler shows that there are sets which have all the
bisecting chords of the same length, and which are smaller than the ball:
these sets are often referred to as Zindler sets. A big work has been done
in last decades to study the properties of the convex sets with respect to
the minimal bisecting length, in particular in the case of Zindler sets, but
the problem of Santalo' is still open. We give the answer of this problem in
the class of Zindler sets.