Asked by john
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 external-secant theorem: (external part) × (whole secant) is equal for both secants.
For SV: external part WV = 6, whole secant SV = SW + WV = (y+4) + 6 = y + 10.
For TV: external part UV = 8, whole secant VT = TU + UV = (y−2) + 8 = y + 6.
Set 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.
For SV: external part WV = 6, whole secant SV = SW + WV = (y+4) + 6 = y + 10.
For TV: external part UV = 8, whole secant VT = TU + UV = (y−2) + 8 = y + 6.
Set 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.
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