Answer:
[tex]\begin{gathered} y=2 \\ RS=RT=10 \end{gathered}[/tex]Step-by-step explanation:
The two tangent theorem states that if there are two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same. This can be represented by the following:
Therefore, we can equalize the expressions of the lengths to find y:
[tex]5y=3y+4[/tex]Solve for y.
[tex]\begin{gathered} 5y-3y=4 \\ 2y=4 \\ y=\frac{4}{2} \\ y=2 \end{gathered}[/tex]Hence, to calculate the length of the indicated segments, we need to substitute y=2 into the expressions:
[tex]\begin{gathered} RS=5y \\ RS=10 \\ \\ RT=3y+4 \\ RT=3(2)+4 \\ RT=10 \end{gathered}[/tex]
