Consider points $O, A, B, C, D$ and $R$ in the diagram below, such that $AR = 4, BR = 2, CR = 2,$ and $DR = 6$:

Question

[asy]
size(250);
import TrigMacros;
import olympiad;

pair O, A, B, C, D, R;
O = (0,0);
A = 3*dir(-40);
B = A + 6*dir(100);
R = 1/3*A + 2/3*B;
C = R - 2dir(10);
D = 4R - 3C;

rr_cartesian_axes(-3, 10, -3, 8, usegrid = false);

draw(A--B);
draw(C--D);

dot("$A$", A, E);
dot("$B$", B, N);
dot("$C$", C, NW);
dot("$D$", D, NE);
dot("$R$",R, SE);
dot("$O$",O, SW);
[/asy]If there exists a real number $t$ such that
\[(1-t) \overrightarrow{OA} + t \overrightarrow{OB} = (1-t) \overrightarrow{OC} + t \overrightarrow{OD},\]enter $t$ below. If this is impossible, enter a question mark.

Answer 1

what an incomprehensible mess, and no diagram.