Answer:
6
Step-by-step explanation:
When you draw two secants to a circle from one exterior point as indicated in the Figure below, then the product of the external segment and the total length of each secant are equal, in other words:
[tex]\overline{AB}. \overline{AD}=\overline{AC}. \overline{AE}[/tex]
Since in this problem we have a tangent line, from the figure we have:
[tex]\overline{AC}. \overline{BC}=\overline{CE}. \overline{CE} \\ \\ \overline{CE}^2=\overline{AC}. \overline{BC} \\ \\ \overline{CE}=\sqrt{\overline{AC}. \overline{BC}} \\ \\ \overline{CE}=\sqrt{12\times 3}=\sqrt{36} \\ \\ \therefore \boxed{ \overline{CE}=6}[/tex]
