  We perform a smoothed analysis of the GCC-condition number C(A) of the linear
programming feasibility problem \exists x\in\R^{m+1} Ax < 0. Suppose that
\bar{A} is any matrix with rows \bar{a_i} of euclidean norm 1 and,
independently for all i, let a_i be a random perturbation of \bar{a_i}
following the uniform distribution in the spherical disk in S^m of angular
radius \arcsin\sigma and centered at \bar{a_i}. We prove that E(\ln C(A)) =
O(mn / \sigma). A similar result was shown for Renegar's condition number and
Gaussian perturbations by Dunagan, Spielman, and Teng [arXiv:cs.DS/0302011].
Our result is robust in the sense that it easily extends to radially symmetric
probability distributions supported on a spherical disk of radius
\arcsin\sigma, whose density may even have a singularity at the center of the
perturbation. Our proofs combine ideas from a recent paper of B\"urgisser,
Cucker, and Lotz (Math. Comp. 77, No. 263, 2008) with techniques of Dunagan et
al.
