Question

HELP! Solve for x. Make sure to show your work and provide complete geometric explanations.

Answer 1

For a.
`x=7`

For b.
`x=2`

Explanation:

To solve this, we are using the intersecting secants theorem. The theorem says that if two secant segments intersect a circle from an exterior point, then the product of the measures of the exterior segment and the whole secant is equal to the product of the measures of the other exterior segment and its whole secant.

Applying this to our circles:

For a.

`5(5+x)=6(6+4)`

`25+5x=6(10)`

`25+5x=60`

`5x=60-25`

`5x=35`

`x=(35)/(5)`

`x=7`

For b.

`4(4+x)=3(3+5)`

`16+4x=3(8)`

`16+4x=24`

`4x=8`

`x=(8)/(4)`

`x=2`

We can conclude that the value of x in (a) is 7, and the value of x in (b) is 2