Answer:
NM = 15
Step-by-step explanation:
Given a secant and a tangent from an external point to the circle, then
The square of the measure of the tangent is equal to the product of the secant's external part and the entire secant, that is
(x + 3)² = (x - 3)(x - 3 + 16)
(x + 3)² = (x - 3)(x + 13) ← expand both sides using FOIL
x² + 6x + 9 = x² + 10x - 39 ( subtract x² + 10x from both sides )
- 4x + 9 = - 39 ( subtract 9 from both sides )
- 4x = - 48 ( divide both sides by - 4 )
x = 12
Then
NM = x + 3 = 12 + 3 = 15
