We know that the line segment drawn from the center of circle to any chord , bisects the chord
So the other part fo the chord is also 6.5
And the radius is 8
, So we can now apply the pythagorean theorem , in the triangle
So
![x^(2)+6.5^(2) = 8^2](https://img.qammunity.org/2019/formulas/mathematics/high-school/8cetlj9u7q1cekmn66gxdj5gcliplnvh9c.png)
![x^2 = 64 - 42.25](https://img.qammunity.org/2019/formulas/mathematics/high-school/60xqrcxr69yahqfdtfxtplks9of6nyvvl1.png)
![x^2 = 21.75](https://img.qammunity.org/2019/formulas/mathematics/high-school/sqw49v4id6pl8k2wqmbqfq20gfwfl9ytyq.png)
taking square root on both sides
x = 4.6637
x=4.7