Q:

Find the circumference

A,B,C, are points on the circle. Point D is the center of the circle. Chord AB is $6\sqrt{2}$. Segment AB and Segment BC is perpendicular.
Can I find the circumference of the given circle, using the given information above only?
I tried this problem, but I made a conclusion that I need an extra piece of information. How do you guys think?

A:

$AB \perp BC$ doesn't tell us anything.  That would be true of any circle (assuming that $A,D,C$ are colinear and $D$ is the center [so $ADC$ is a diameter).
So all this tells us is that the circle has a chord of $6\sqrt 2$ but any circle with a diameter of $6\sqrt 2$ will have a chord of $6\sqrt 2$ so all we can conclude is the diameter is at least $6\sqrt 2$.
If we know some more information such as $AC\perp DB$ or $AB = BC$ (btw $AC\perp DB \iff AB=BC$) then we could solve it.  Are you sure the problem was written correctly?  Perhaps the book mad an error and we were suppose to be told $AD \perp DB$?
If that were the case then as $AD,DB, DC$ are equal length radii and $\triangle ADB$ is right triangle we have $AD^2 + DB^2 = (6\sqrt 2)^2$ and that's easily solved that $AD = 6$.  

