Question

Find the value of x. What is the value of x?

Answer 1

x = 16

Explanation:

The product of the lengths theorem is a property that can be sued to describe the relationships of the sides between the tangents and secants in a circle. One of these products states the following;

The distance between the point of tangency and its intersection point with the exterior secant squared is equal to the product of the exterior secant times the interior secant.

This essentially means the following equation can be formed;

`(AB)^2=(DC)(CB)`

Substitute,

`12^2=x*9`

Simplify,

`144=9x`

Inverse operations,

`(144)/(9)=x\\\\16=x`

Answer 2

`\boxed{\sf x=7}`

Explanation:

By Targent-secant theorem...

`\sf 9(x + 9) = {12}^(2)`

Use the distributive property to multiply 9 by x+9.

`\sf 9x+81= {12}^(2)`

Now, let calculate 12 to the power of 2 and get 144.

`\sf 9x+81=144`

Subtract 81 from both sides.

`\sf 9x=63`

Divide both sides by 9.

`\sf \cfrac{ 9x}{9} = \cfrac{63}{9}`

`\sf x=7`