Secant and tangent theorem: Square of measure of tangent is equal to the product of length of whole secant and length of exterior secant segment, i.e.
[tex] \text{ tangent}^2=\text{whole secant}\cdot \text{exterior secant} [/tex].
The whole secant with exterior secant 5 in is 5+y in. Using this theorem you can state that
[tex] 9^2=(5+y)\cdot 5 [/tex].
Solve this equation:
[tex] 81=25+5y,\\ 5y=81-25,\\ 5y=56,\\ y=11.2 [/tex] in.
Answer: y=11.2 in.
