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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_3 / A 3−4−5 right triangle is inscribed in circle A, and a 5−12−13 right triangle is inscribed in circle B. Find the ratio of the area of circle A to the area of circle B. The final an…

Problem

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

problem

3-4-5

right triangle is inscribed in circle

A

, and a

5-12-13

right triangle is inscribed in circle

B

. Find the ratio of the area of circle

A

to the area of circle

B

. The final answer can be written in the form

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. What is

m+n

Plain-text mathematical notation (without MathML)

A 3−4−5 right triangle is inscribed in circle A, and a 5−12−13 right triangle is inscribed in circle B. Find the ratio of the area of circle A to the area of circle B. The final answer can be written in the form (m)/(n), where m and n are relatively prime positive integers. What is m+n?

Original LaTeX notation

A $3-4-5$ right triangle is inscribed in circle $A$, and a $5-12-13$ right triangle is inscribed in circle $B$. Find the ratio of the area of circle $A$ to the area of circle $B$. The final answer can be written in the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_3
task_id: a04c0259-e923-5194-93f7-03b793c59475
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12B~5fProblems~2fProblem~5f3
task_revision_id: 2
config / split: default / train

Official source

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