Answer:
[tex]FC=25.9[/tex]
Step-by-step explanation:
Congruent Triangles
The figure shows two triangles FCD and FED. One of their sides is the radius of the circle, they both form a 90° angle with the line CD and ED and they share the same segment FD.
Thus, both triangles are congruent and we have the length of a side (12 units), one common side (the hypotenuse) and one unknown leg that must be equal. Therefore
[tex]13x-16=4x+11[/tex]
Solving
[tex]9x=27[/tex]
[tex]x=3[/tex]
The required side FD is the hypotenuse of any of the triangles. The unknown leg can be calculated by
[tex]13x-16=23[/tex]
Or
[tex]4x+11=23[/tex]
Thus
[tex]FD^2=12^2+23^2=673[/tex]
Solving
[tex]FD=\sqrt{673}[/tex]
[tex]\boxed{FC=25.9}[/tex]
