2011 AIME II Problem 13

Point P lies on the diagonal A C of square A B C D with A P>C P. Let O_{1} and O_{2} be the circumcenters
of triangles A B P and C D P, respectively. Given that A B=12 and \angle O_{1} P O_{2}=120^{\circ}, then A P=\sqrt{a}+\sqrt{b},
where a and b are positive integers. Find a+b.