Question

GEOMETRY ASSISTANCE NEEDED?

Answer 1

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.

`\text{ tangent}^2=\text{whole secant}\cdot \text{exterior secant}`.

The whole secant with exterior secant 5 in is 5+y in. Using this theorem you can state that

`9^2=(5+y)\cdot 5`.

Solve this equation:

`81=25+5y,\\ 5y=81-25,\\ 5y=56,\\ y=11.2` in.

Answer: y=11.2 in.