Question

Refer to the figure to find the following measure. 8 M If AB = 6, BC =6, and DC = 4, then EC = 18 O9

Answer 1

When we have chords like these, we can relate the lengths of the sides as:

$BC\cdot AC=DC\cdot EC$

We can replace this with the infromation we have as:

$\begin{gathered} BC\cdot AC=DC\cdot EC \\ BC\cdot(BC+AB)=DC\cdot EC \\ 6\cdot(6+6)=4\cdot EC \\ 6\cdot12=4\cdot EC \\ 72=4\cdot EC \\ EC=\frac{72}{4} \\ EC=18 \end{gathered}$

Answer: EC = 18