Answer:
YZ = 44
Step-by-step explanation:
Let the intersection of XW and YZ equal A. For this problem, we can use power of a point in the scenario where two secants intersect in the interior of a circle. We get the equation:
WA * AX = ZA * AY
We can substitute the values we are given to get:
(2x - 6)(21) = (x + 1)(30)
42x - 126 = 30x + 30
12x - 126 = 30
12x = 156
x = 13
Using segment addition postulate, we can say that:
YZ = YA + AZ
And we can plug in what we know from the diagram:
YZ = 30 + x + 1
We can also plug in the value of x, 13
YZ = 30 + 13 + 1 = 44
