Question

For circle H, JN = x, NK = 2, LN = 3, and NM = 6. Solve for x.

a) 1
b) 7
c) 9
d) 4

Answer 1

To solve for x, use the tangent-secant theorem to set up and solve an equation.

Step-by-step explanation:

To solve for x, we can use the property of the tangent and secant segments of a circle. Segment JN is a tangent to circle H, while segment LN and NM are secants. According to the tangent-secant theorem, the product of the lengths of the secant segment LN and its external segment NM is equal to the product of the lengths of the whole secant segment JN and its external segment NK. Using this theorem, we can set up the equation 3 * 6 = x * (x + 2) and solve for x.

3 * 6 = x * (x + 2)

18 = x^2 + 2x

x^2 + 2x - 18 = 0

(x - 3)(x + 6) = 0

x = 3 or x = -6

Since lengths cannot be negative, the only valid solution is x = 3.