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USAMO 1984 Problem 3

  • Day 1
  • Answer

A,B,C,D,XA, B, C, D, X are five points in space, such that AB,BC,CD,DAA B, B C, C D, D A all subtend the acute angle θ\theta at XX. Find the maximum and minimum possible values of ∠AXC+∠BXD\angle \mathrm{AXC}+\angle \mathrm{BXD} (for all such configurations) in terms of θ\theta.

Dataset text NuminaMath olympiads. Quoted with source.

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2 \cos ^{-1}(2 \cos \theta-1)

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