In the diagram below, angle PQR = angle PRQ = angle STR = angle TSR, RQ = 8 and SQ = 2. Find PQ.
Diagram Link:
https://latex.artofproblemsolving.com/4/3/0/4302d19b0763e32ee077a4add3ad46f7bc977ea2.png
Code for Diagram (in case link doesn't work):
[asy]
pair A,B,C,D,E;
A = (0, 0.9);
B = (-0.4, 0);
C = (0.4, 0);
D = (-0.275, 0.16);
E = (0.11, 0.65);
draw(A--B);
draw(A--C);
draw(B--C);
draw(B--E);
draw(C--D);
label("$P$",A,N);
label("$Q$", B, S);
label("$R$", C, S);
label("$S$", D, S);
label("$T$", E, W);
[/asy]
