Answer:
NM = 15
Step-by-step explanation:
There is a property of secants and tangents to a circle where:
The square of the tangent length is equal the length of the external segment of the secant times the whole secant length.
Therefore, in our question, we have that:
[tex]NM^2 = ML * MK[/tex]
The values of NM, ML and MK are:
[tex]NM = x + 3[/tex]
[tex]ML = x - 3[/tex]
[tex]MK = ML + LK = x - 3 + 16 = x + 13[/tex]
So we have:
[tex](x+3)^2 = (x - 3)(x + 13)[/tex]
[tex]x^2 + 6x + 9 = x^2 + 10x - 39[/tex]
[tex]6x + 9 = 10x - 39[/tex]
[tex]4x = 48[/tex]
[tex]x = 12[/tex]
So the length of NM is:
[tex]NM = x + 3 = 12 + 3 = 15[/tex]
