Answer:
[tex]r=10.4[/tex]Step-by-step explanation:
We can find the radius of the circle using the Pythagorean theorem, let's see the following diagram to understand:
Since the triangles show above has to be congruent, it means we can equalize the expressions (4x-5) and (x+4) to find x:
[tex]\begin{gathered} 4x-5=x+4 \\ 4x-x=4+5 \\ 3x=9 \\ x=\frac{9}{3} \\ x=3 \end{gathered}[/tex]Now, use the Pythagorean theorem to find the radius:
[tex]\begin{gathered} r^2=3^2+10^2 \\ r=\sqrt[]{9+100} \\ r=\sqrt[]{109} \\ r=10.4 \end{gathered}[/tex]