In △ABC, AB=8, BC=7, CA=6 and side BC is extended, as shown in the figure, to a point P so that △PAB is similar to △PCA. The length of PC is[asy]
size(200);
defaultpen(linewidth(0.7)+fontsize(10));
pair A=origin, P=(1.5,5), B=(8,0), C=P+2.5*dir(P--B);
draw(A--P--C--A--B--C);
label("A", A, W);
label("B", B, E);
label("C", C, NE);
label("P", P, NW);
label("6", 3*dir(A--C), SE);
label("7", B+3*dir(B--C), NE);
label("8", (4,0), S);[/asy]
<spanclass=′latex−bold′>(A)</span>7<spanclass=′latex−bold′>(B)</span>8<spanclass=′latex−bold′>(C)</span>9<spanclass=′latex−bold′>(D)</span>10<spanclass=′latex−bold′>(E)</span>11