  In this paper we will show the duality between the range test (RT) and
no-response test (NRT) for the inverse boundary value problem for the Laplace
equation in $\Omega\setminus\overline D$ with an obstacle $D\Subset\Omega$
whose boundary $\partial D$ is visible from the boundary $\partial\Omega$ of
$\Omega$ and a measurement is given as a set of Cauchy data on
$\partial\Omega$. Here the Cauchy data is given by a unique solution $u$ of the
boundary value problem for the Laplace equation in $\Omega\setminus\overline D$
with homogeneous and inhomogeneous Dirichlet boundary condition on $\partial D$
and $\partial\Omega$, respectively. These testing methods are domain sampling
method to estimate the location of the obstacle using test domains and the
associated indicator functions. Also both of these testing methods can test the
analytic extension of $u$ to the exterior of a test domain. Since these methods
are defined via some operators which are dual to each other, we could expect
that there is a duality between the two methods. We will give this duality in
terms of the equivalence of the pre-indicator functions associated to their
indicator functions. As an application of the duality, the reconstruction of
$D$ using the RT gives the reconstruction of $D$ using the NRT and vice versa.
We will also give each of these reconstructions without using the duality if
the Dirichlet data of the Cauchy data on $\partial\Omega$ is not identically
zero and the solution to the associated forward problem does not have any
analytic extension across $\partial D$. Moreover, we will show that these
methods can still give the reconstruction of $D$ if $D$ is a convex polygon and
it satisfies one of the following two properties: all of its corner angles are
irrational and its diameter is less than its distance to $\partial\Omega$.
