Given an Orthogonal-Buekenhout-Metz unital $U_{α,β}$, embedded in $PG(2,q^2)$, and a point $P\notin U_{α,β}$, we study the set of feet, $τ_{P}(U_{α,β})$, of $P$ in $U_{α,β}$. We characterize geometrically each of these sets as either $q+1$ collinear points or as $q+1$ points partitioned into two arcs. Other results about the geometry of these sets are also given.