Answer:
C
Step-by-step explanation:
∠ ABC = 90° ( angle in a semicircle )
Using the cosine ratio in right triangle ABC and the exact value
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos30° = [tex]\frac{adjacent }{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{10}{AC}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
AC × [tex]\sqrt{3}[/tex] = 20 ( divide both sides by [tex]\sqrt{3}[/tex] )
AC = [tex]\frac{20}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] ( rationalising denominator )
AC = [tex]\frac{20\sqrt{3} }{3}[/tex]
radius AO = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × [tex]\frac{20\sqrt{3} }{3}[/tex] = [tex]\frac{10\sqrt{3} }{3}[/tex] → C