Question

What is the measure of SR?

Answer 1

RS = 8

Explanation:

Given:

Secant QU = internal secant segment PU + external secant segment PQ = 7 + 9 = 16

Secant QS = internal secant segment RS + external secant segment RQ = (3x - 5) + 8

To find the measure of RS, we need to find the value of x.

Thus, recall the "Two Secant Theorem"

According to the theorem,

(RS + RQ)*RQ = (PU + PQ)*PQ

Thus,

`(3x - 5 + 8)*8 = (7 + 9)*9`

`(3x + 3)*8 = (16)*9`

`24x + 24 = 144`

Subtract 24 from both sides

`24x + 24 - 24 = 144 - 24`

`24x = 120`

Divide both sides by 24

`(24x)/(24) = (120)/(24)`

`x = 5`

Plug in the value of x into (3x - 5) to find the measure of RS

RS = 3(5) - 5 = 15 - 7

RS = 8