Question

Solve for the value of x

Answer 1

Answer:

x = 2

Step-by-step 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

Answer 2

Answer:

$x=2$

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 ($secant_A$) 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,

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

$6x+12=12x$

$12=6x$

$x=2$