Question

A circle is shown. 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 T U is y minus 2, the length of U V is 8, the length of S W is y +4, and the length of W V is 6. What is the length of line segment SV? 6 units 8 units 12 units 16 units

Answer 1

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;

$WV \times SV=UV \times TV$

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.

Answer 2

Answer:

16

Step-by-step explanation:

16