Given:
Secants S V and T V intersect at point V outside of the circle. Secant S V intersects the circle at point W. Secant T V intersects the circle at point U.
The length of TU is (y - 2).
The length of UV is 8.
The length of SW is (y + 4)
The length of WV is 6.
We need to determine the length of line segment SV.
Value of y:
The value of y can be determined using the intersecting secant theorem.
Applying, the theorem, we get;
[tex]WV \times SV=UV \times TV[/tex]
Substituting the values, we have;
[tex]6 \times (y+4+6)=8 \times (y-2+8)[/tex]
[tex]6 \times (y+10)=8 \times (y+6)[/tex]
[tex]6y+60=8y+48[/tex]
[tex]-2y+60=48[/tex]
[tex]-2y=-12[/tex]
[tex]y=6[/tex]
Thus, the value of y is 6.
Length of SV:
The length of SV is given by
[tex]SV=SW+WV[/tex]
[tex]SV=y+4+6[/tex]
[tex]SV=6+4+6[/tex]
[tex]SV=16[/tex]
Thus, the length of SV is 16 units.
Hence, Option D is the correct answer.
