Question

Please Help me Find NM using Secant

Answer 1

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:

$NM^2 = ML * MK$

The values of NM, ML and MK are:

$NM = x + 3$

$ML = x - 3$

$MK = ML + LK = x - 3 + 16 = x + 13$

So we have:

$(x+3)^2 = (x - 3)(x + 13)$

$x^2 + 6x + 9 = x^2 + 10x - 39$

$6x + 9 = 10x - 39$

$4x = 48$

$x = 12$

So the length of NM is:

$NM = x + 3 = 12 + 3 = 15$