Question

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

Answer 1

Option C.

Explanation:

From the given figure it is clear that

`PQ=5,QR=7,PS=4,ST=x`

So,

`PR=PQ+QP=5+7=12`

`PT=PS+ST=4+x`

Using Intersecting Secants Theorem, we get

`PQ* PR=PS* PT`

`5* 12=4* (4+x)`

`60=16+4x`

`60-16+4x`

`44=4x`

Divide both sides by 4.

`11=x`

`PT=4+x=4+11=15`

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