  Let $\Omega$ be a bounded convex domain in $\mathbb{R}^n$ ($n \ge 2$). In
this work, we prove that if there exists an integrable function $f$ such that
it's Radon transform over $(n-1)$-dimensional hyperplanes intersecting the
domain $\Omega$ is a strictly positive function of distance to the nearest
parallel supporting hyperplane to $\Omega$, then $\Omega$ is a ball and the
function $f$ is a unique radial function about the centre of $\Omega$.
