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;

$WV \times SV=UV \times TV$

Substituting the values, we have;

$6 \times (y+4+6)=8 \times (y-2+8)$

$6 \times (y+10)=8 \times (y+6)$

$6y+60=8y+48$

$-2y+60=48$

$-2y=-12$

$y=6$

Thus, the value of y is 6.

Length of SV:

The length of SV is given by

$SV=SW+WV$

$SV=y+4+6$

$SV=6+4+6$

$SV=16$

Thus, the length of SV is 16 units.

Hence, Option D is the correct answer.

7 0

3 years ago

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castortr0y [4]

The Answer Is D (4hrs 25min)
Hope This Helps!

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