Answer:
[tex]AC=8inches[/tex]
Step-by-step explanation:
It is given that triangle AOC intersects a circle with center O, side AO is 10 inches and the diameter of the circle is 12 inches, thus
OC is the radius of the circle and is equal to [tex]\frac{D}{2}=\frac{12}{2}=6 inches[/tex].
Now, From ΔAOC, using the Pythagoras theorem, we get
[tex](OA)^{2}=(OC)^{2}+(AC)^{2}[/tex]
⇒[tex](10)^{2}=(6)^2+(AC)^2[/tex]
⇒[tex]100=36+(AC)^2[/tex]
⇒[tex]64=(AC)^2[/tex]
⇒[tex]AC=8inches[/tex]
