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USAMO 1984 Problem 3 - Optimize <APC+<BPD

Source: USAMO 1984 Problem 3

August 16, 2011
AMCUSA(J)MOUSAMOgeometry unsolvedgeometry

Problem Statement

P,A,B,C,P, A, B, C, and DD are five distinct points in space such that ∠APB=∠BPC=∠CPD=∠DPA=θ\angle APB = \angle BPC = \angle CPD = \angle DPA = \theta, where θ\theta is a given acute angle. Determine the greatest and least values of ∠APC+∠BPD\angle APC + \angle BPD.
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