su and vt are chords that intersect at point r. what is the length of line segment vt? 4 units 8 units 13…

Explanation:

Step1: Apply the intersecting - chords theorem

According to the intersecting - chords theorem, when two chords $\overline{SU}$ and $\overline{VT}$ intersect at a point $R$ inside a circle, we have $SR\times RU=VR\times RT$. So, $(x + 6)\times x=(x + 1)\times(x + 4)$.

Step2: Expand both sides of the equation

Expand the left - hand side: $(x + 6)\times x=x^{2}+6x$. Expand the right - hand side: $(x + 1)\times(x + 4)=x^{2}+4x+x + 4=x^{2}+5x + 4$.

Step3: Solve the equation

Set the two expanded expressions equal: $x^{2}+6x=x^{2}+5x + 4$. Subtract $x^{2}$ from both sides of the equation, we get $6x=5x + 4$. Then subtract $5x$ from both sides, and $x = 4$.

Step4: Calculate the length of $\overline{VT}$

The length of $\overline{VT}=(x + 1)+(x + 4)$. Substitute $x = 4$ into the expression: $(4 + 1)+(4 + 4)=5 + 8=13$.

Answer:

13 units