Referring to the Segment Lengths in Circles, given the figure below:
[tex]ab=cd[/tex]
Now, applying this to our problem,
[tex]3x-5(12)=15(8)[/tex][tex]3x-5=\frac{15(8)}{12}[/tex][tex]3x-5=10[/tex][tex]3x=10+5[/tex][tex]x=\frac{15}{3}[/tex][tex]x=5[/tex]
Now, given this, we will now be able to solve for the length of FD.
[tex]FD=3x-5+12[/tex][tex]=3(5)-5+12[/tex][tex]=15-5+12[/tex][tex]=10+12_{}[/tex][tex]FD=22[/tex]
Therefore, FD is equal to 22 units.
