In right △ABC with legs 5 and 12, arcs of circles are drawn, one with center A and radius 12, the other with center B and radius 5. They intersect the hypotenuse at M and N. Then, MN has length:[asy]size(200);
defaultpen(linewidth(0.7)+fontsize(10));
pair A=origin, B=(12,7), C=(12,0), M=12*dir(A--B), N=B+B.y*dir(B--A);
real r=degrees(B);
draw(A--B--C--cycle^^Arc(A,12,0,r)^^Arc(B,B.y,180+r,270));
pair point=incenter(A,B,C);
label("A", A, dir(point--A));
label("B", B, dir(point--B));
label("C", C, dir(point--C));
label("M", M, dir(point--M));
label("N", N, dir(point--N));label("12", (6,0), S);
label("5", (12,3.5), E);[/asy]<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>513<spanclass=′latex−bold′>(C)</span>3<spanclass=′latex−bold′>(D)</span>4<spanclass=′latex−bold′>(E)</span>524