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

Problem

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problem

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.
Plain-text mathematical notation (without MathML)
P,A,B,C, and D are five distinct points in space such that ∠APB=∠BPC=∠CPD=∠DPA=θ, where θ is a given acute angle. Determine the greatest and least values of ∠APC+∠BPD.
Original LaTeX notation
$P, A, B, C,$ and $D$ are five distinct points in space such that $\angle APB = \angle BPC = \angle CPD = \angle DPA = \theta$, where $\theta$ is a given acute angle. Determine the greatest and least values of $\angle APC + \angle BPD$.

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Source and history

task_id
5809f8a6-04ca-5a5a-a2c3-4e751c9fed89
task_key
test--5809f8a6-04ca-5a5a-a2c3-4e751c9fed89
task_revision_id
1
config / split
/ test

Official source

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