[asy]
import cse5;
size(180);
real a=4, b=3;
pathpen=black;
pair A=(a,0), B=(0,b), C=(0,0);
D(MP("A",A)--MP("B",B,N)--MP("C",C,SW)--cycle);
pair X=IP(B--A,(0,0)--(b,a));
D(CP((X+C)/2,C));
D(MP("R",IP(CP((X+C)/2,C),B--C),NW)--MP("Q",IP(CP((X+C)/2,C),A--C+(0.1,0))));
//Credit to chezbgone2 for the diagram[/asy]
In △ABC, AB=10AC=8 and BC=6. Circle P is the circle with smallest radius which passes through C and is tangent to AB. Let Q and R be the points of intersection, distinct from C , of circle P with sides AC and BC, respectively. The length of segment QR is<spanclass=′latex−bold′>(A)</span>4.75<spanclass=′latex−bold′>(B)</span>4.8<spanclass=′latex−bold′>(C)</span>5<spanclass=′latex−bold′>(D)</span>42<spanclass=′latex−bold′>(E)</span>33