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2006 AMC 12B Question 15

AMC12 · 2006 AMC 12B

Question 15

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

Question illustration
  1. $18\sqrt{3}$
  2. $24\sqrt{2}$
  3. $36$
  4. $24\sqrt{3}$
  5. $32\sqrt{2}$