For a compact set Γ⊂R2 and a point x, we define the visible part of Γ from x to be the set
Γx={u∈Γ:[x,u]∩Γ={u}}.
(Here [x,u] denotes the closed line segment joining x to u.)
In this paper, we use energies to show that if Γ is a compact connected set of Hausdorff dimension larger than one, then for (Lebesgue) almost every point x∈R2, the Hausdorff dimension of Γx is strictly
less than the Hausdorff dimension of Γ. In fact, for almost every x,
dimH(Γx)≤21+dimH(Γ)−43.
We also give an estimate of the Hausdorff dimension of those points
where the visible set has dimension larger than σ+21+dimH(Γ)−43 for σ>0