When we have chords like these, we can relate the lengths of the sides as:
[tex]BC\cdot AC=DC\cdot EC[/tex]We can replace this with the infromation we have as:
[tex]\begin{gathered} BC\cdot AC=DC\cdot EC \\ BC\cdot(BC+AB)=DC\cdot EC \\ 6\cdot(6+6)=4\cdot EC \\ 6\cdot12=4\cdot EC \\ 72=4\cdot EC \\ EC=\frac{72}{4} \\ EC=18 \end{gathered}[/tex]Answer: EC = 18
