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2017 AMC 10B Problem 22

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2017 AMC 10B Problem 22AMC 10 Step by Step

Name: Date: September 13, 2026

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

The diameter $AB$ of a circle of radius $2$ is extended to a point $D$ outside the circle so that $BD=3$ . Point $E$ is chosen so that $ED=5$ and line $ED$ is perpendicular to line $AD$ . Segment $AE$ intersects the circle at a point $C$ between $A$ and $E$ . What is the area of $\triangle ABC$ ?

A)
$\frac{120}{37}$
B)
$\frac{140}{39}$
C)
$\frac{145}{39}$
D)
$\frac{140}{37}$
E)
$\frac{120}{31}$

2017 AMC 10B Problem 22

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