  In metric Diophantine approximation there are two main types of
approximations: simultaneous and dual for both homogeneous and inhomogeneous
settings. The well known measure-theoretic theorems of Khintchine and Jarn\'ik
are fundamental in these settings. Recently, there has been substantial
progress towards establishing a metric theory of Diophantine approximations on
manifolds. In particular, both the Khintchine and Jarn\'ik type results have
been established for planar curves except for only one case. In this paper, we
prove an inhomogeneous Jarn\'ik type theorem for convergence on planar curves
and in so doing complete the metric theory for both the homogeneous and
inhomogeneous settings for approximation on planar curves.
