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2004 AMC 10A Problem 22

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2004 AMC 10A Problem 22AMC 10 Step by Step

Name: Date: September 13, 2026

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

Square $ABCD$ has side length $2$ . A semicircle with diameter $\overline{AB}$ is constructed inside the square, and the tangent to the semicircle from $C$ intersects side $\overline{AD}$ at $E$ . What is the length of $\overline{CE}$ ?

A)
$\frac{2+\sqrt{5}}{2}$
B)
$\sqrt{5}$
C)
$\sqrt{6}$
D)
$\frac{5}{2}$
E)
$5-\sqrt{5}$

2004 AMC 10A Problem 22

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