Question

Solve for x.
solve for x.
solve for x.

Answer 1

`x=10`

Explanation:

A secant is a line segment that intersects a circle in two places. One property of a secant is the product of the lengths ratio. This ratio can be described as the following, let (
`inside`) refer to the part of the secant that is inside the circle, and (
`outside`) refer to the part that is outside of it. (
`total`) will refer to the entirety of the secant or (
`inside+outside`). The numbers (1) and (2) will be used as subscripts to indicate that there are two different secants.

`(outside_1)(total_2)=(outside_2)(total_2)`

Substitute,

`(outside_1)(total_2)=(outside_2)(total_2)`

`(outside_1)(inside_1+outisde_1)=(outside_2)(inside_2+outside_2)`

`(6)(6+x+5)=(7)(7+x+1)`

Simplify,

`(6)(6+x+5)=(7)(7+x+1)`

`6(x+11)=7(x+8)`

`6x+66=7x+56`

Inverse operations,

`6x+66=7x+56`

`66=x+56`

`10=x`