To find the length of $WX$ in the given diagram, we can use the Power of a Point theorem, which states that for a point $P$ outside a circle, the product of the lengths of the segments of any secant line passing through $P$ is equal to the square of the length of the tangent segment from $P$ to the circle.

In this problem, point $X$ is outside the circle, and $ZX$ is the secant line intersecting the circle at points $Z$ and $Y$. $WX$ is the tangent line from $X$ to the circle.

The Power of a Point theorem can be written as: $WX^2 = XY \cdot XZ$

From the diagram:

• $XY = 15$
• $XZ = XY + YZ = 15 + 29 = 44$

We can now substitute these values into the equation: $WX^2 = 15 \cdot 44$ $WX^2 = 660$

Taking the square root of both sides to find $WX$: $WX = \sqrt{660}$ $WX \approx 25.7$

So, the length of $WX$ is approximately 25.7 units.

Would you like further details on any part of this solution or have any additional questions?

Here are some questions you might want to ask:

1. How do you derive the Power of a Point theorem?
2. Can you explain the steps for solving similar problems with different given values?
3. What are some other applications of the Power of a Point theorem?
4. How can this theorem be applied in three-dimensional geometry?
5. What are other important theorems related to circles?

Tip: Always double-check your calculations and ensure you understand the underlying principles behind the formulas you use.