  We study continuum percolation problem of overlapping discs with a
distribution of radii having a power-law tail; the probability that a given
disc has a radius between $R$ and $R+dR$ is proportional to $R^{-(a+1)}$, where
$a > 2$. We show that in the low-density non-percolating phase, the two-point
function shows a power law decay with distance, even at arbitrarily low
densities of the discs, unlike the exponential decay in the usual percolation
problem. As in the problem of fluids with long-range interaction, we argue that
in our problem, the critical exponents take their short range values for $a > 3
- \eta_{sr}$ whereas they depend on $a$ for $a < 3-\eta_{sr}$ where $\eta_{sr}$
is the anomalous dimension for the usual percolation problem. The mean-field
regime obtained in the fluid problem corresponds to the fully covered regime,
$a \leq 2$, in the percolation problem. We propose an approximate
renormalization scheme to determine the correlation length exponent $\nu$ and
the percolation threshold. We carry out Monte-Carlo simulations and determine
the exponent $\nu$ as a function of $a$. The determined values of $\nu$ show
that it is independent of the parameter $a$ for $a>3 - \eta_{sr}$ and is equal
to that for the lattice percolation problem, whereas $\nu$ varies with $a$ for
$2<a<3 - \eta_{sr}$. We also determine the percolation threshold of the system
as a function of the parameter $a$.
