IMO 1982 LL BRA10

Let r1, . . . , rn be the radii of n spheres. Call S1, S2, . . . , Sn the

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IMO 1982 LL BRA10

Origin: BRA

Problem

Let r1, . . . , rn be the radii of n spheres. Call S1, S2, . . . , Sn the areas of the set of points of each sphere from which one cannot see any point of any other sphere. Prove that S1 r2

  • S2 r2
  • \cdot \cdot \cdot + Sn r2n = 4\pi.