Answer
$BC=6\sqrt 2$
Work Step by Step
Given that $OC$ and $OB$ are both radii, and both equal $6$; and also given that $\overline{OC}\bot\overline{AB}$, we end up with an isosceles right triangle, $\triangle COB$. This is also a 45-45-90 Triangle, which means that if $OC=OB=6$, then the hypotenuse $BC=6\sqrt 2$.
Or we could use Pythagorean's Theorem.
$6^{2}+6^{2}=c^{2}$
$36+36=c^{2}$
$72=c^{2}$
$c=6\sqrt 2$
