Let $T=TNFTPP$.  Points $A$ and $B$ lie on a circle centered at $O$ such that $\angle AOB$ is right.  Points $C$ and $D$ lie on radii $OA$ and $OB$ respectively such that $AC = T-3$, $CD = 5$, and $BD = 6$.  Determine the area of quadrilateral $ACDB$.

[asy]
draw(circle((0,0),10));
draw((0,10)--(0,0)--(10,0)--(0,10));
draw((0,3)--(4,0));
label("O",(0,0),SW);
label("C",(0,3),W);
label("A",(0,10),N);
label("D",(4,0),S);
label("B",(10,0),E);
[/asy]

[b]Note: This is part of the Ultimate Problem, where each question depended on the previous question.  For those who wanted to try the problem separately, [hide=here's the value of T]$T=10$[/hide].