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The original publication is available at www.springerlink.comInternational audienceWe show that if a line L is an isolated line transversal to a finite family F of (possibly intersecting) balls in R^3 and no two balls are externally tangent on L, then there is a subfamily G ⊆ F of size at most 12 such that L is an isolated line transversal to G. We generalize this result to families of semialgebraic ovaloids

Pinning a Line by Balls or Ovaloids in ℝ3