  Given an open neighborhood $W$ of the zero section in the cotangent bundle of
$N$ we define a distance-like function $\rho_W$ on $N$ using certain symplectic
embeddings from the standard ball $B^{2n}(r)$ to $W$. We show that when $W$ is
the unit disc-cotangent bundle of a Riemannian metric on $N$, $\rho_W$ recovers
the metric. As an intermediate step, we give a new construction of the ball of
capacity 4 to the product of Lagrangian discs $P_L := B^n(1)\times B^n(1)$, and
we give a new proof of the strong Viterbo conjecture about normalized
capacities for $P_L$. We also give bounds of the symplectic packing number of
two balls in a unit disc-cotangent bundle relative to the zero section $N$.
