  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 $R^d$, 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
$\epsilon$-far from being $(k,G)$-clusterable. A set $S$ is $\epsilon$-far
$(0<\epsilon\leq1)$ from being $(k,G)$-clusterable if at least $\epsilon n$
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.
