So the solution to this problem says:
$x^2=8(9)$
$x^2=72$
$x=\sqrt{72}$
which means $CE=\sqrt{72}=6\sqrt{2}$
I'm a bit confuse with the solution. I am assuming that $CE=x$ and $ED=x$ as well because of the intersecting chord theorem which says (for this case):
$(CE)(ED)=(AE)(EB)$
However, what I don't understand is how do we know that the length of $CE$ is the same length as $ED$. Shouldn't each be represented by different variables?
I think the clue is in the fact that "AB is a bisector of CD" which generally means that AB divides CD into two equal halves. This means $CE = ED$.