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2006 AMC 10B Problem 24

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2006 AMC 10B Problem 24AMC 10 Step by Step

Name: Date: September 13, 2026

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

Circles with centers $O$ and $P$ have radii $2$ and $4$ , respectively, and are externally tangent. Points $A$ and $B$ on the circle with center $O$ and points $C$ and $D$ on the circle with center $P$ are such that $AD$ and $BC$ are common external tangents to the circles. What is the area of the concave hexagon $AOBCPD$ ?

A)
$18\sqrt{3}$
B)
$24\sqrt{2}$
C)
$36$
D)
$24\sqrt{3}$
E)
$32\sqrt{2}$

2006 AMC 10B Problem 24

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