AMC 12 2006a Problem 13

The vertices of a $3-4-5$ right triangle are the centers of three mutually externally tangent circles, as shown. What is the sum of the areas of the three circles?

unitsize(5mm);
defaultpen(fontsize(10pt)+linewidth(.8pt));
pair B=(0,0), C=(5,0);
pair A=intersectionpoints(Circle(B,3),Circle(C,4))[0];
draw(A--B--C--cycle);
draw(Circle(C,3));
draw(Circle(A,1));
draw(Circle(B,2));
label("$A$",A,N);
label("$B$",B,W);
label("$C$",C,E);
label("3",midpoint(B--A),NW);
label("4",midpoint(A--C),NE);
label("5",midpoint(B--C),S);

$\mathrm{(A) \ } 12\pi \mathrm{(B) \ } \frac{25\pi}{2} \mathrm{(C) \ } 13\pi \mathrm{(D) \ } \frac{27\pi}{2} \mathrm{(E) \ } 14\pi$