Review circle relationships as you answer the questions below.

1. On your paper, draw a diagram of $⊙B$ with $\overarc { A C }$. If $m\overarc { A C }= 80°$ and the length of the radius of $⊙B$ is $10$, what is the length of chord $\overline{AC}$?

   Hint (a):

   What do you notice about $BA$ and $BC$?

   More Help (a):

   How can trigonometry help you solve for $AC$?

2. Now draw a diagram of a circle with two chords, $\overline{EF}$ and $\overline{GH}$, that intersect at point $K$. If $EF = 15$, $EK = 6$, and $HK = 3$, what is $GK$?

   Hint (b):

   

   More Help (b):

   Remember that intersecting chords create similar
   triangles, and that the corresponding sides of similar
   triangles have equal ratios.

   Step (b):

   $\frac{9}{3}=\frac{x}{6}$