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2023 AMC 10A Problem 22

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2023 AMC 10A Problem 22AMC 10 Step by Step

Name: Date: September 13, 2026

Circles · difficulty 4 of 5 · about 6 min · position P21-25

Circle $C_1$ and $C_2$ each have radius $1$ , and the distance between their centers is $\frac{1}{2}$ . Circle $C_3$ is the largest circle internally tangent to both $C_1$ and $C_2$ . Circle $C_4$ is internally tangent to both $C_1$ and $C_2$ and externally tangent to $C_3$ . What is the radius of $C_4$ ?

A)
$\frac{1}{14}$
B)
$\frac{1}{12}$
C)
$\frac{1}{10}$
D)
$\frac{3}{28}$
E)
$\frac{1}{9}$

2023 AMC 10A Problem 22

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