The point vortex system is usually considered as an idealized model where the
vorticity of an ideal incompressible two-dimensional fluid is concentrated in a
finite number of moving points. In the case of a single vortex in an otherwise
irrotational ideal fluid occupying a bounded and simply-connected
two-dimensional domain the motion is given by the so-called Kirchhoff-Routh
velocity which depends only on the domain. The main result of this paper
establishes that this dynamics can also be obtained as the limit of the motion
of a rigid body immersed in such a fluid when the body shrinks to a massless
point particle with fixed circulation. The rigid body is assumed to be only
accelerated by the force exerted by the fluid pressure on its boundary, the
fluid velocity and pressure being given by the incompressible Euler equations,
with zero vorticity. The circulation of the fluid velocity around the particle
is conserved as time proceeds according to Kelvin's theorem and gives the
strength of the limit point vortex. We also prove that in the different regime
where the body shrinks with a fixed mass the limit dynamics is governed by a
second-order differential equation involving a Kutta-Joukowski-type lift force
