Answer:
WX = 6
Step-by-step explanation:
1. Approach
First, one must find the value of the variable (x). This can be done by using the Tangent-Line-intersection-theorem (many people refer to it by another name, but the theory is the same). This theory essentially states that when two lines are tangent to a circle and are non-parallel, the distance between the point of tangency, and the point of intersection of those two lines are the same for each line. After finding the value of (x), one can substitute it back into the given equation for the value of (WX), and solve it.
2. Finding (x)
The two segments; (WX) and (XY) are tangent to the given circle. Meaning that they only make contact with the circle at a single point. The space between their point of tangency and the point at which they intersect will be equal. Essentially meaning that the length of (WX) and the length of (XY) are the same. Therefore the equation
(XY) = (XW)
Can be formed. Substitute in the given values;
7x - 29 = 2x + 16
Inverse operations,
7x - 29 = 2x + 16
-2x -2x
5x - 29 = 16
+29 +29
5x = 45
/5 /5
x = 9
3. Solve for (WX)
Now substitute back in to find the length of (WX)
7x = 29
x = 5
7(5) - 29
35 - 29
6
