Question

Solve for x




please help! I'm so confused​

Answer 1

a.
`x=7`

b.
`x=2`

Explanation:

We have been given a graph of two circles and we are asked to solve for x.

a. We can see that x and 4 are secants of our given triangle, which intersect outside our given triangle, so we will use intersecting secants theorem to find the value of x.

Intersecting secants theorem states that when two secants intersect outside the circle, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

Using intersecting theorem we can set an equation as:

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

Let us solve for x.

`5x+25=10*6`

`5x+25-25=60-25`

`5x=35`

Let us divide both sides of our equation by 5.

`(5x)/(5)=(35)/(5)`

`x=7`

Therefore, value of x is 7.

b. Using intersecting secants theorem we can set an equation for our bigger circle as:

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

Let us solve for x.

`8*3=4x+16`

`24-16=4x+16-16`

`8=4x`

Let us divide both sides of our equation by 4.

`(8)/(4)=(4x)/(4)`

`2=x`

Therefore, the value of x for bigger circle is 2.