Respuesta :

Answer:

RS = 8

Step-by-step 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,

[tex] (3x - 5 + 8)*8 = (7 + 9)*9 [/tex]

[tex] (3x + 3)*8 = (16)*9 [/tex]

[tex] 24x + 24 = 144 [/tex]

Subtract 24 from both sides

[tex] 24x + 24 - 24 = 144 - 24 [/tex]

[tex] 24x = 120 [/tex]

Divide both sides by 24

[tex] \frac{24x}{24} = \frac{120}{24} [/tex]

[tex] x = 5 [/tex]

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

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

RS = 8

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