Answer:
6.4
Step-by-step explanation:
Since we can assume that JK is tangent to the circle, we can identify that JKL is a right triangle. Therefore, we can apply the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
where:
[tex]a[/tex] and [tex]b[/tex] are the legs (shorter sides) and [tex]c[/tex] is the hypotenuse.
Plugging in the given side lengths, we get:
[tex]9.6^2 + (JL)^2 = 16^2[/tex]
which we can use to solve for JL:
[tex](JL)^2 = 16^2 - 9.6^2[/tex]
[tex]JL = \sqrt{16^2 - 9.6^2}[/tex]
[tex]\boxed{JL=12.8}[/tex]
We know that JL is the diameter of the circle, or twice the radius. We are asked to solve for ML, which is the radius, so we need to divide JL by 2:
[tex]ML = \dfrac{JL} 2[/tex]
[tex]ML = \dfrac{12.8} 2[/tex]
[tex]\boxed{ML=6.4}[/tex]
