Answer:
The length of radius AO is;
![18.4\operatorname{cm}]()
Step-by-step explanation:
Let C represent the point at which the line from the center intersect the chord AB.
Given;
![\begin{gathered} AB=32\operatorname{cm} \\ OC=9\operatorname{cm} \end{gathered}]()
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;
![\begin{gathered} AC=(AB)/(2) \\ AC=\frac{32\operatorname{cm}}{2} \\ AC=16\operatorname{cm} \end{gathered}]()
Since AOC form a right angled triangle, we can apply pythagoras theorem to calculate the radius AO;
![\begin{gathered} AO^2=OC^2+AC^2 \\ AO=\sqrt[]{OC^2+AC^2} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/3841xfm9in5vp80s27hrs1946rons40v9p.png)
substituting the values we have;
![\begin{gathered} AO=\sqrt[]{9^2+16^2} \\ AO=\sqrt[]{81+256} \\ AO=18.36\operatorname{cm} \\ AO=18.4\operatorname{cm} \end{gathered}]()
The length of radius AO is;
![18.4\operatorname{cm}]()