A circle is shown. Secants S V and T V intersect at point V outside of the circle. Secant S V intersects the circle at point W. Secant T V intersects the circle at point U. The length of T U is y minus 2, the length of U V is 8, the length of S W is y +4, and the length of W V is 6.
What is the length of line segment SV?

Step-by-step explanation:

we know that

The Intersecting Secants Theorem, states that: If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

so

In this problem

we have

substitute the given values

solve for y

Find the length of segment SV

substitute the value of y

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: