Helly's theorem is a fundamental result in discrete geometry, describing the
ways in which convex sets intersect with each other. If S is a set of n
points in Rd, we say that S is (k,G)-clusterable if it can be
partitioned into k clusters (subsets) such that each cluster can be contained
in a translated copy of a geometric object G. In this paper, as an
application of Helly's theorem, by taking a constant size sample from S, we
present a testing algorithm for (k,G)-clustering, i.e., to distinguish
between two cases: when S is (k,G)-clusterable, and when it is
ϵ-far from being (k,G)-clusterable. A set S is ϵ-far
(0<ϵ≤1) from being (k,G)-clusterable if at least ϵn
points need to be removed from S to make it (k,G)-clusterable. We solve
this problem for k=1 and when G is a symmetric convex object. For k>1, we
solve a weaker version of this problem. Finally, as an application of our
testing result, in clustering with outliers, we show that one can find the
approximate clusters by querying a constant size sample, with high probability