  If the Radon transform of a compactly supported distribution $f \ne 0$ in
$\mathbb R^n$ is supported on the set of tangent planes to the boundary
$\partial D$ of a bounded convex domain $D$, then $\partial D$ must be an
ellipsoid. As a corollary of this result we get a new proof of a recent theorem
of Koldobsky, Merkurjev, and Yaskin, which settled a special case of a
conjecture of Arnold that was motivated by a famous lemma of Newton.
