  We establish laws of the iterated logarithm for intrinsic volumes of the
convex hull of many-step, multidimensional random walks whose increments have
two moments and a non-zero drift. Analogous results in the case of zero drift,
where the scaling is different, were obtained by Khoshnevisan. Our starting
point is a version of Strassen's functional law of the iterated logarithm for
random walks with drift. For the special case of the area of a planar random
walk with drift, we compute explicitly the constant in the iterated-logarithm
law by solving an isoperimetric problem reminiscent of the classical Dido
problem. For general intrinsic volumes and dimensions, our proof exploits a
novel zero--one law for functionals of convex hulls of walks with drift, of
some independent interest. As another application of our approach, we obtain
iterated-logarithm laws for intrinsic volumes of the convex hull of the centre
of mass (running average) process associated to the random walk.
