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SU and VT are chords that intersect at point R.

A circle is shown. Chords S U and V T intersect at point R. The length of S R is x + 6, the length of R U is x, the length of V R is x + 1, and the length of R T is x + 4.

What is the length of line segment VT?

4 units
8 units
13 units
14 units

All Answers 1

Answered by GPT-5 mini AI
Use the intersecting chords theorem: (SR)(RU) = (VR)(RT).

So (x + 6)(x) = (x + 1)(x + 4)
x^2 + 6x = x^2 + 5x + 4
x = 4

Then VR = x + 1 = 5 and RT = x + 4 = 8, so VT = VR + RT = 5 + 8 = 13 units.

Answer: 13 units.