Question

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

Answer 1

Answer:

$x=10$

Step-by-step 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,

$6x+66=7x+56$

$66=x+56$

$10=x$