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Omni-MATH / Let ABCD be a regular tetrahedron, and let O be the centroid of triangle BCD. Consider the point P on AO such that P minimizes PA+2(PB+PC+PD). Find sin∠PBO.

Problem

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problem

Let ABCDABCD be a regular tetrahedron, and let OO be the centroid of triangle BCDBCD. Consider the point PP on AOAO such that PP minimizes PA+2(PB+PC+PD)PA+2(PB+PC+PD). Find sin∠PBO\sin \angle PBO.
Plain-text mathematical notation (without MathML)
Let ABCD be a regular tetrahedron, and let O be the centroid of triangle BCD. Consider the point P on AO such that P minimizes PA+2(PB+PC+PD). Find sin∠PBO.
Original LaTeX notation
Let $ABCD$ be a regular tetrahedron, and let $O$ be the centroid of triangle $BCD$. Consider the point $P$ on $AO$ such that $P$ minimizes $PA+2(PB+PC+PD)$. Find $\sin \angle PBO$.

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Source and history

task_id
3e890cd8-cb03-5d43-9817-e189a3baa7c8
task_key
test--3e890cd8-cb03-5d43-9817-e189a3baa7c8
task_revision_id
1
config / split
/ test

Official source

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