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Identify the value of x and the length of each secant segment. HELP PLS options: x = 15; PR = 12; PT = 19 x = 15; PR = 19; PT = 12 x = 11; PR = 12; PT = 15 x = 11; PR = 15; PT = 12

Identify the value of x and the length of each secant segment. HELP PLS options: x = 15; PR = 12; PT = 19 x = 15; PR = 19; PT = 12 x = 11; PR = 12; PT = 15 x = class=

Answer :

Answer:

Option C.

Step-by-step explanation:

From the given figure it is clear that

[tex]PQ=5,QR=7,PS=4,ST=x[/tex]

So,

[tex]PR=PQ+QP=5+7=12[/tex]

[tex]PT=PS+ST=4+x[/tex]

Using Intersecting Secants Theorem, we get

[tex]PQ\times PR=PS\times PT[/tex]

[tex]5\times 12=4\times (4+x)[/tex]

[tex]60=16+4x[/tex]

[tex]60-16+4x[/tex]

[tex]44=4x[/tex]

Divide both sides by 4.

[tex]11=x[/tex]

[tex]PT=4+x=4+11=15[/tex]

Since, x = 11; PR = 12; PT = 15, therefore the correct option is C.

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