Answer:
[tex]x=2[/tex]
Step-by-step explanation:
The term 'secant' refers to a line segment that intersects a circle in two places. When two secants intersect inside a circle, one can use the product of lengths theory to form ratios between the parts of intersection between the secants. This ratio can be described as the following, let ([tex]secant_A[/tex]) and ([tex]secant_B[/tex]) represent the two secants in the circle. Part (1) and (2) will refer to the two parts formed after the intersection of the secants.
[tex](secant_A_1)(secant_A_2)=(secant_B_1)(secant_B_2)[/tex]
Use this formula in the given situation, substitute the given values in and solve for the unknown,
[tex](secant_A_1)(secant_A_2)=(secant_B_1)(secant_B_2)[/tex]
[tex](6)(x+2)=(12)(x)[/tex]
Simplify,
[tex](6)(x+2)=(12)(x)[/tex]
[tex]6x+12=12x[/tex]
[tex]12=6x[/tex]
[tex]x=2[/tex]
