Mock AIME 6 2006-2007 Problems/Problem 13

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 intersects 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 $PBA$ ?