Answer:
[tex]x=2\frac{1}{3}\ in[/tex]
Step-by-step explanation:
we know that
In the given circle, the segment CD is a diameter (because is a chord that passes through the center E)
The given diameter is [tex]D=36\ in[/tex]
The radius of the circle is half the diameter
so
[tex]r=36/2=18\ in[/tex]
we have
[tex]EF=3x+11[/tex]
Remember that the distance from the center to any point on the circle is equal to the radius of the circle
so
The length of segment EF is equal to the radius
[tex]3x+11=18[/tex]
solve for x
[tex]3x=18-11\\3x=7\\x=\frac{7}{3}\ in[/tex]
Convert to mixed number
[tex]x=\frac{7}{3}=\frac{6}{3}+\frac{1}{3}=2\frac{1}{3}\ in[/tex]
