Question

if secant segments sr and tr intersect at point r, find the length of vt. start by relating the secants and segments theorem to this diagram. (rs)( )=( )(rv). substitute values from the diagram into the equation. (16)( )=( )(8). solve for vt. vt = 4 25 4 75 12

Explanation:

Step1: Recall secant - secant rule

If two secant segments are drawn to a circle from an exterior point, then $(RS)(RU)=(RT)(RV)$.

Step2: Identify lengths from the diagram

We know that $RS = 6 + 10=16$, $RU = 6$, $RT=8 + VT$, $RV = 8$.
Substituting into the secant - secant formula: $(16)(6)=(8 + VT)(8)$.

Step3: Solve the equation

First, calculate the left - hand side: $16\times6 = 96$.
The equation becomes $96=(8 + VT)\times8$.
Divide both sides by 8: $\frac{96}{8}=8 + VT$.
$12=8 + VT$.
Subtract 8 from both sides: $VT=12 - 8 = 4$.

Answer:

4