IT-CESENATICO 1993 Problem 1

Let be given points $A,B,C$ on a line, with $C$ between $A$ and $B$ . Three semicircles with diameters $AC,BC,AB$ are drawn on the same side of line $ABC$ . The perpendicular to $AB$ at $C$ meets the circle with diameter $AB$ at $H$ . Given that $CH =\sqrt2$ , compute the area of the region bounded by the three semicircles.