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Omni-MATH / Suppose point P is inside triangle ABC. Let AP,BP, and CP intersect sides BC,CA, and AB at points D,E, and F, respectively. Suppose ∠APB=∠BPC=∠CPA,PD=(1)/(4),PE=(1)/(5), and …

Problem

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problem

Suppose point PP is inside triangle ABCABC. Let AP,BPAP, BP, and CPCP intersect sides BC,CABC, CA, and ABAB at points D,ED, E, and FF, respectively. Suppose ∠APB=∠BPC=∠CPA,PD=14,PE=15\angle APB=\angle BPC=\angle CPA, PD=\frac{1}{4}, PE=\frac{1}{5}, and PF=17PF=\frac{1}{7}. Compute AP+BP+CPAP+BP+CP.
Plain-text mathematical notation (without MathML)
Suppose point P is inside triangle ABC. Let AP,BP, and CP intersect sides BC,CA, and AB at points D,E, and F, respectively. Suppose ∠APB=∠BPC=∠CPA,PD=(1)/(4),PE=(1)/(5), and PF=(1)/(7). Compute AP+BP+CP.
Original LaTeX notation
Suppose point \(P\) is inside triangle \(ABC\). Let \(AP, BP\), and \(CP\) intersect sides \(BC, CA\), and \(AB\) at points \(D, E\), and \(F\), respectively. Suppose \(\angle APB=\angle BPC=\angle CPA, PD=\frac{1}{4}, PE=\frac{1}{5}\), and \(PF=\frac{1}{7}\). Compute \(AP+BP+CP\).

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Source and history

task_id
b4548a74-20a2-5d54-acf7-59925e57a5bf
task_key
test--b4548a74-20a2-5d54-acf7-59925e57a5bf
task_revision_id
1
config / split
/ test

Official source

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