Mock AIME 6 2006-2007 Problems/Problem 13

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Problem

Consider two circles of different sizes that do not intersect. The smaller circle has center $O$. Label the intersection of their common external tangents $P$. A common internal tangent interesects the common external tangents at points $A$ and $B$. Given that the radius of the larger circle is $11$, $PO=3$, and $AB=20\sqrt{2}$, what is the square of the area of triangle $PBA$?

Solution

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