Explanation
A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency
For the given question, we will have
Then, we can solve for r
Where r is the radius of the circle
[tex](r+15)^2=r^2+25^2[/tex]
So that
[tex]\left(r+15\right)^2=r^2+625[/tex][tex]r^2+30r+225-225=r^2+625-225[/tex][tex]r^2+30r=r^2+400[/tex][tex]\begin{gathered} 30r=400 \\ \\ r=\frac{40}{3} \end{gathered}[/tex]
Thus, the diameter which is twice the radius will be
[tex]diameter=2\times\frac{40}{3}=\frac{80}{3}=26.67[/tex]
The diameter is approximately 26.7
