Question

Solve for the value of x

Answer 1

`x=2`

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 (
`secant_A`) and (
`secant_B`) represent the two secants in the circle. Part (1) and (2) will refer to the two parts formed after the intersection of the secants.

`(secant_A_1)(secant_A_2)=(secant_B_1)(secant_B_2)`

Use this formula in the given situation, substitute the given values in and solve for the unknown,

`(secant_A_1)(secant_A_2)=(secant_B_1)(secant_B_2)`

`(6)(x+2)=(12)(x)`

Simplify,

`(6)(x+2)=(12)(x)`

`6x+12=12x`

`12=6x`

`x=2`

Answer 2

x = 2

Explanation:

Given 2 intersecting chords in a circle, then

The product of the parts of one chord is equal to the product of the parts of the other chord , that is

12x = 6(x + 2) = 6x + 12 ( subtract 6x from both sides )

6x = 12 ( divide both sides by 6 )

x = 2