Branchwidth of Graphs and Matroids were introduced by Robertson and Seymour in their Graph Minor X paper. In 2002, Geelen, Gerards, Robertson and Whittle asked whether the branchwidth of a bridgeless graph is equal to the branchwidth of its cycle matroid. With Frederic Mazoit, we give a positive answer to this question. A straightforward corollary being that the branchwidth of a planar bridgeless graph is equal to the branchwidth of its dual.