Question

Acellus - Angle Measures and Segment Length

Wanted to share this:
p(p+q) = r(r+s)

In this case, solve for s, or x.
Please don't take this down, I'm just tryna pass on knowledge for anyone looking for this!

Answer 1

We have been given diagram of a circle and its secants. We are asked to find the value of x.

We will use secant-secant theorem to solve our given problem.

When two secants share a common end-point outside circle, then the product of one secant segment and its external segment is equal to the product of other secant segment and its external segment.

Using secant-secant theorem, we will get an equation:

`6\cdot(12+6)=5\cdot (5+x)`

Let us solve for x.

`6\cdot(18)=25+5x`

`108=25+5x`

`25+5x=108`

`25-25+5x=108-25`

`5x=83`

`(5x)/(5)=(83)/(5)`

`x=16.6`

Therefore, the value of x is 16.6 cm.