Question

1. What is the value of n?

Answer 1

N=5
AC = 33
AC = 150

Explanation:
If two chords intersect inside a circle, the products of their segments is equal.  For this circle, this means that
(n+1)(18)=(n+7)(9)

Using the distributive property on both sides,
n*18+1*18 = n*9+7*9
18n+18=9n+63

Subtract 9n from both sides:
18n+18-9n=9n+63-9n
9n+18=63

Subtract 18 from both sides:
9n+18-18=63-18
9n=45

Divide both sides by 9:
9n/9 = 45/9
n=5

The measure of an inscribed angle is equal to half of the measure of the intercepted arc.  For the second image, this means that
2.5x+4=1/2(7x-2)

Using the distributive property: 
2.5x+4=1/2(7x)-1/2(2)
2.5x+4=3.5x-1

Subtract 2.5x from both sides:
2.5x+4-2.5x=3.5x-1-2.5x
4=1x-1

Add 1 to both sides:
4+1=1x
5=1x
5=x

Substitute this in for x in AC:
7x-2=7*5-2=35-2=33

For the third image, we have
75=1/2(AC)

Multiplying both sides by 2:
75*2=AC
150=AC