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2021 AMC Fall 10A Problem 19

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2021 AMC Fall 10A Problem 19AMC 10 Step by Step

Name: Date: September 13, 2026

Circles · difficulty 4 of 5 · about 7 min · position P16-20

A disk of radius $1$ rolls all the way around the inside of a square of side length $s>4$ and sweeps out a region of area $A$ . A second disk of radius $1$ rolls all the way around the outside of the same square and sweeps out a region of area $2A$ . The value of $s$ can be written as $a+\frac{b\pi}{c}$ , where $a,b$ , and $c$ are positive integers and $b$ and $c$ are relatively prime. What is $a+b+c$ ?

A)
$10$
B)
$11$
C)
$12$
D)
$13$
E)
$14$

2021 AMC Fall 10A Problem 19

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