Task 130

The task

What is the shortest distance that can be travelled if you start at any point, $A$, $B$, $C$, or $D$, and visit the other three points once? [asy] pair A,B,C, D; A = (-3,3); B = (3,0); C = (0, -4); D = (0,0); draw(D--B--C--cycle); draw(D--A--B--cycle);draw(D--A--C--cycle); label("$A$", A, NW);label("$B$", B, E); label("$C$", C, S);label("$D$", D, NE); label("3", D--B, S); label("6", A--B, NE); label("6", A--C, SW); label("4", D--C, NW+N); label("5", A--D, SE+NE); label("5", C--B, E); [/asy]