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Tetrahedral Minimization

Source:

April 6, 2008
geometry3D geometrytetrahedrontrigonometrycalculusderivative

Problem Statement

Let ABCD ABCD be a regular tetrahedron, and let O O be the centroid of triangle BCD BCD. Consider the point P P on AO AO such that P P minimizes PA \plus{} 2(PB \plus{} PC \plus{} PD). Find sin⁡∠PBO \sin \angle PBO.
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