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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_19 / In △ABC medians (AD)¯ and (BE)¯ intersect at G and △AGE is equilateral. Then cos(C) can be written as (m√(p))/(n), where m and n are relatively prime positive integers and p is a p…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

\triangle{ABC}

medians

\overline{AD}

and

\overline{BE}

intersect at

G

and

\triangle{AGE}

is equilateral. Then

\cos(C)

can be written as

\frac{m\sqrt p}n

, where

m

and

n

are relatively prime positive integers and

p

is a positive integer not divisible by the square of any prime. What is $m+n+p?$

Plain-text mathematical notation (without MathML)

In △ABC medians (AD)¯ and (BE)¯ intersect at G and △AGE is equilateral. Then cos(C) can be written as (m√(p))/(n), where m and n are relatively prime positive integers and p is a positive integer not divisible by the square of any prime. What is $m+n+p?$

Original LaTeX notation

In $\triangle{ABC}$ medians $\overline{AD}$ and $\overline{BE}$ intersect at $G$ and $\triangle{AGE}$ is equilateral. Then $\cos(C)$ can be written as $\frac{m\sqrt p}n$, where $m$ and $n$ are relatively prime positive integers and $p$ is a positive integer not divisible by the square of any prime. What is $m+n+p?$

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_19
task_id: 7785c1e0-ec5b-57cf-b369-f406ecb7ad80
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f19
task_revision_id: 2
config / split: default / train

Official source

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