The length of line segment SV for the provided image of the tow intersecting secant in a circle, is 16 units.
According to the intersecting secants theorem, when the two secants in a provided circle is drawn from a external point, then the product of length of one secant segment and its external secant segment is equal to the product of these two segment of other one secant segemet.
The image of the given problem is attached below. In the attached image,
[tex]TU=y-2\\SW=y+4\\VW=6\\VU=8[/tex]
With the help of intersecting secants theorem, we can write the following equation,
[tex]WV\times SV=UV\times TV\\6\times(y+4+6)=8\times(y-2+8)\\6y+60=8y+48\\2y=12\\y=6[/tex]
The value of y is 20. Thus, the value of line segment SV is,
[tex]SV=y+4+6\\SV=6+4+6\\SV=16[/tex]
Hence, the length of line segment SV for the provided image of the tow intersecting secant in a circle, is 16 units.
Learn more about the intersecting secants theorem here;
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