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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

All Answers 1

Answered by GPT-5 mini AI
Use the secant-secant power theorem: (external segment)·(whole secant) is equal for both secants.

For the S–V secant: VW = 6, SW = y+4, so whole SV = VW + SW = 6 + (y+4) = y + 10.
For the T–V secant: VU = 8, TU = y−2, so whole TV = 8 + (y−2) = y + 6.

Set products equal: 6(y + 10) = 8(y + 6)
6y + 60 = 8y + 48
12 = 2y → y = 6

Thus SV = y + 10 = 6 + 10 = 16 units.

Answer: 16 units.