Notice that the triangle ABC is a right triangle, and the radius of the circle is equal to the length of the segment AB.
To compute the length of the segment AB we will use the Pythagorean theorem:
[tex]c^2=a^2+b^2,[/tex]
where c is the length of the hypotenuse and a, and b are the lengths of the legs.
Substituting:
[tex]\begin{gathered} c=AC=16, \\ a=BC=13, \\ b=AB \end{gathered}[/tex]
we get:
[tex]16^2=13^2+AB^2.[/tex]
Solving the above equation for AB, we get:
[tex]AB=\sqrt{16^2-13^2}.[/tex]
Therefore:
[tex]AB=\sqrt{87}\approx9.3.[/tex]
Answer:
[tex]9.3\text{ }[/tex]
