Answer:
The length of radius AO is;
[tex]18.4\operatorname{cm}[/tex]
Explanation:
Let C represent the point at which the line from the center intersect the chord AB.
Given;
[tex]\begin{gathered} AB=32\operatorname{cm} \\ OC=9\operatorname{cm} \end{gathered}[/tex]
we can see that the line from the center forms a right angle with the chord AB at point C.
So, the length AC will be half of Chord AB;
[tex]\begin{gathered} AC=\frac{AB}{2} \\ AC=\frac{32\operatorname{cm}}{2} \\ AC=16\operatorname{cm} \end{gathered}[/tex]
Since AOC form a right angled triangle, we can apply pythagoras theorem to calculate the radius AO;
[tex]\begin{gathered} AO^2=OC^2+AC^2 \\ AO=\sqrt[]{OC^2+AC^2} \end{gathered}[/tex]
substituting the values we have;
[tex]\begin{gathered} AO=\sqrt[]{9^2+16^2} \\ AO=\sqrt[]{81+256} \\ AO=18.36\operatorname{cm} \\ AO=18.4\operatorname{cm} \end{gathered}[/tex]
The length of radius AO is;
[tex]18.4\operatorname{cm}[/tex]
