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2005 AMC 10A Problem 23

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2005 AMC 10A Problem 23AMC 10 Step by Step

Name: Date: September 13, 2026

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

Let $\overline{AB}$ be a diameter of a circle and $C$ be a point on $\overline{AB}$ with $2 \cdot AC = BC$ . Let $D$ and $E$ be points on the circle such that $\overline{DC} \perp \overline{AB}$ and $\overline{DE}$ is a second diameter. What is the ratio of the area of $\triangle DCE$ to the area of $\triangle ABD$ ?

A)
$\frac{1}{6}$
B)
$\frac{1}{4}$
C)
$\frac{1}{3}$
D)
$\frac{1}{2}$
E)
$\frac{2}{3}$

2005 AMC 10A Problem 23

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