  Suppose that $C\subset\mathbb P^2$ is a general enough nodal plane curve of
degree $>2$, $\nu\colon \hat C\to C$ is its normalization, and $\pi\colon \hat
C\to\mathbb P^1$ is a finite morphism simply ramified over the same set of
points as a projection $\mathrm{pr}_p\circ \nu\colon\hat C \to\mathbb P^1$,
where $p\in\mathbb P^2\setminus C$ (if $\mathrm{deg}\, C=3$, one should assume
in addition that $\deg\pi\ne4$). We prove that the morphism $\pi$ is equivalent
to such a projection if and only if it extends to a finite morphism
$X\to(\mathbb P^2)^*$ ramified over $C^*$, where $X$ is a smooth surface.
  As a by-product, we prove the Chisini conjecture for mappings ramified over
duals to general nodal curves of any degree $\ge3$ except for duals to smooth
cubics; this strengthens one of Victor Kulikov's results.
