  In this note we introduce a pseudometric on convex planar curves based on
distances between normal lines and show its basic properties. Then we use this
pseudometric to give a short proof of the theorem by Pinchasi that the sum of
perimeters of $k$ convex planar bodies with disjoint interiors contained in a
convex body of perimeter $p$ and diameter $d$ is not greater than $p+2(k-1)d$.
