In the circle above, chord $\overline{AB}$ is extended to meet the tangent $\overline{DE}$ at D. If $\overline{AB}=12\ cm$ and $\overline{DE}=8\ cm$, find the length of $\overline{BD}$

A

$$4\sqrt{6}\ cm$$

B

$$5\ cm$$

C

$$4\ cm$$

D

$$6\ cm$$