Question

Point O is the center of the circle. Chord AB has length 32 cm and the distance from the center of the circle to chord AB is 9cm. A What is the length of radius AO (to the nearest tenth)?

Answer 1

The length of radius AO is;

Step-by-step explanation:

Let C represent the point at which the line from the center intersect the chord AB.

Given;

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;

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}`

substituting the values we have;

The length of radius AO is;