To solve for $x$ in the given problem, we can recognize that the diagram relates to a tangent-segment theorem and applies the power of a point property. Let’s proceed step by step.

Step 1: Understand the relationship

• The triangle $MNL$ involves segment $ML = x$, $MN = 16$, and $NL = 12$.
• The segment $NL$ (12) connects point $N$ to a point on the circle, while $ML$ lies along a straight line, intersecting the tangent.

By the power of a point theorem, for a point external to a circle: $\text{(tangent segment)}^2 = \text{(secant segment)} \times \text{(external part of the secant)}.$

Step 2: Apply the power of a point

Here:

• $ML = x$ is the external segment.
• $MN = 16$ is the total length of the secant.
• $NL = 12$, part of the secant.

Thus, using: [ ML^2 = MN \times (MN - NL). The