Question

What is the value of n? Enter your answer in the box.

Answer 1

`n=6`

Explanation:

We have been given an image of a circle. We are asked to find the value of n.

We can see that two chords of our given circle are intersecting inside it, so we will use intersecting chords theorem to solve for n.

Intersecting chords theorem states that when two chords of a circle intersect inside the circle, then product of the segments of both chords is equal.

Using intersecting chords theorem we can set an equation as:

`5(n+8)=7(n+4)`

Using distributive property
`a(b+c)=a*b+a*c` we will get,

`5*n+5*8=7*n+7*4`

`5n+40=7n+28`

Subtracting 40 and 7n from both sides we will get,

`5n-7n+40-40=7n-7n+28-40`

`-2n=-12`

Dividing both sides by -2 we will get,

`(-2n)/(-2)=(-12)/(-2)`

`n=6`

Therefore, the value of n is 6.

Answer 2

n=6

Explanation:

Since, we know that when two chords intersect each other inside a circle, the products of their segments are equal. Thus, using this property, we have

`(n+8)5=(n+4)7`

⇒
`5n+40=7n+28`

⇒
`40-28=7n-5n`

⇒
`12=2n`

⇒
`n=6`

Thus, the value of n is 6.