NL-NWO 2010 Problem 1

Consider a triangle $ABC$ such that $\angle A = 90^o, \angle C =60^o$ and $|AC|= 6$ . Three circles with centers $A, B$ and $C$ are pairwise tangent in points on the three sides of the triangle. Determine the area of the region enclosed by the three circles (the grey area in the figure).