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Omni-MATH / Consider a variable point P inside a given triangle ABC. Let D, E, F be the feet of the perpendiculars from the point P to the lines BC, CA, AB, respectively. Find all points P whi…

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problem

Consider a variable point PP inside a given triangle ABCABC. Let DD, EE, FF be the feet of the perpendiculars from the point PP to the lines BCBC, CACA, ABAB, respectively. Find all points PP which minimize the sum \[ {BC\over PD}+{CA\over PE}+{AB\over PF}. \]
Plain-text mathematical notation (without MathML)
Consider a variable point P inside a given triangle ABC. Let D, E, F be the feet of the perpendiculars from the point P to the lines BC, CA, AB, respectively. Find all points P which minimize the sum \[ {BC\over PD}+{CA\over PE}+{AB\over PF}.  \]
Original LaTeX notation
Consider a variable point $P$ inside a given triangle $ABC$. Let $D$, $E$, $F$ be the feet of the perpendiculars from the point $P$ to the lines $BC$, $CA$, $AB$, respectively. Find all points $P$ which minimize the sum \[ {BC\over PD}+{CA\over PE}+{AB\over PF}.  \]

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Source and history

task_id
07df1aed-4fef-53c4-a7e2-8a5dd889079a
task_key
test--07df1aed-4fef-53c4-a7e2-8a5dd889079a
task_revision_id
1
config / split
/ test

Official source

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