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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_20 / Isosceles trapezoid ABCD has parallel sides (AD)¯ and (BC)¯, with BC<AD and AB=CD. There is a point P in the plane such that PA=1,PB=2,PC=3, and PD=4. Let (r)/(s)=fracBCAD is irred…

Problem

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problem

Isosceles trapezoid

ABCD

has parallel sides

\overline{AD}

and

\overline{BC},

with

BC < AD

and

AB = CD.

There is a point

P

in the plane such that

PA=1, PB=2, PC=3,

and

PD=4.

Let

\frac{r}{s}=frac{BC}{AD}

is irreducible fraction, what is the value of

r+s

Plain-text mathematical notation (without MathML)

Isosceles trapezoid ABCD has parallel sides (AD)¯ and (BC)¯, with BC<AD and AB=CD. There is a point P in the plane such that PA=1,PB=2,PC=3, and PD=4. Let (r)/(s)=fracBCAD is irreducible fraction, what is the value of r+s?

Original LaTeX notation

Isosceles trapezoid $ABCD$ has parallel sides $\overline{AD}$ and $\overline{BC},$ with $BC < AD$ and $AB = CD.$ There is a point $P$ in the plane such that $PA=1, PB=2, PC=3,$ and $PD=4.$ Let $\frac{r}{s}=frac{BC}{AD}$ is irreducible fraction, what is the value of $r+s$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_20
task_id: 9be6cb75-dd02-5e09-a3d1-a409dc64d854
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f20
task_revision_id: 2
config / split: default / train

Official source

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