Question

su and vt are chords that intersect at point r. what is the length of line - segment vt? 4 units 8 units 13 units 14 units

Explanation:

Step1: Apply the chord - chord intersection theorem

If two chords $SU$ and $VT$ intersect at a point $R$ inside a circle, then $VR\times RT=SR\times RU$.
So, $(x + 1)\times(x + 4)=x\times(x + 6)$.

Step2: Expand both sides

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

Step3: Set up the equation and solve for x

Set $x^{2}+5x + 4=x^{2}+6x$.
Subtract $x^{2}$ from both sides: $5x + 4=6x$.
Subtract $5x$ from both sides to get $x = 4$.

Step4: Find the length of VT

$VT=(x + 1)+(x + 4)$.
Substitute $x = 4$ into the expression: $VT=(4 + 1)+(4 + 4)=5 + 8=14$ units.

Answer:

14 units