% define the end points of the three rays
z1 = right scaled 200 rotated 10;
z2 = right scaled 100 rotated 135;
z3 = right scaled 225 rotated -17.5;
% define the other points, relative to Q
pair A, B, P, Q, R;
Q = 0.8125 z3;
A = whatever[origin, z1]; A-Q = whatever * z1 rotated 90;
P = whatever[origin, z2]; P-Q = whatever * z2 rotated 90;
B = whatever[origin, z1]; B-P = whatever * z1 rotated 90;
R = whatever[A,Q];        R-P = whatever * (B-P) rotated 90;
% mark the angles 
drawoptions(withcolor .67 blue); 
path c; c = fullcircle scaled 30;
draw c rotated angle (Q-P) shifted P cutafter (P--B);
draw c rotated angle (P-Q) shifted Q cutafter (Q--R);
draw c rotated angle P               cutafter (origin--z1);
drawoptions();
% draw the rays and A--Q
drawarrow origin -- z1; label(btex $r_1$ etex, z1 scaled 1.05);
drawarrow origin -- z2; label(btex $r_2$ etex, z2 scaled 1.08);
drawarrow origin -- z3; label(btex $r_3$ etex, z3 scaled 1.05);
draw A--Q;
% draw the dashed lines
drawoptions(dashed evenly);
draw B--P--R--Q--P; drawarrow origin -- P scaled 4/3;
drawoptions();
% label the points
dotlabel.urt(btex $Q$ etex, Q);
dotlabel.top(btex $A$ etex, A);
dotlabel.lrt(btex $R$ etex, R) withcolor .67 blue;
label.top (btex $B$ etex, B);
label.llft(btex $P$ etex, P);
label.llft(btex $O$ etex, origin);