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2006 AMC 10B Problem 19

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2006 AMC 10B Problem 19AMC 10 Step by Step

Name: Date: September 13, 2026

Circles · difficulty 3 of 5 · about 5 min · position P16-20

A circle of radius $2$ is centered at $O$ . Square $OABC$ has side length $1$ . Sides $AB$ and $CB$ are extended past $B$ to meet the circle at $D$ and $E$ , respectively. What is the area of the shaded region in the figure, which is bounded by $BD$ , $BE$ , and the minor arc connecting $D$ and $E$ ?

A)
$\frac{\pi}{3}+1-\sqrt{3}$
B)
$\frac{\pi}{2}(2-\sqrt{3})$
C)
$\pi(2-\sqrt{3})$
D)
$\frac{\pi}{6}+\frac{\sqrt{3}+1}{2}$
E)
$\frac{\pi}{3}-1+\sqrt{3}$

2006 AMC 10B Problem 19

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