Question

Find the value of x
A. 4
B. 9
C. 36
D. 5

Answer 1

`a)\ \ 4`

Explanation:

A secant is a line that intersects a circle in two points. The product of the lengths theorem is a theorem that forms a ratio between the lengths of the secants when two secants intersect in a circle. Let (
`secant_1`) and (
`secant_2`) refer to the entirety of the secants. (
`part_1_a`) and (
`part_1_b`) will refer to the different parts of (
`secant_1`). (
`part_2_a`) and (
`part_2_b`) will refer to the different parts of (
`secant_2`).

`part_1_a*part_1_b=part_2_a*part_2_b`

Substitute with the given values in the problem,
`part_1_a*part_1_b=part_2_a*part_2_b`

`x*9=3*12`

Simplify,

`x*9=3*12`

`9x=36`

Inverse operations,

`9x=36`

`x=4`