Question

10 points

Answer 1

Answer:

$FC=25.9$

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

$13x-16=4x+11$

Solving

$9x=27$

$x=3$

The required side FD is the hypotenuse of any of the triangles. The unknown leg can be calculated by

$13x-16=23$

Or

$4x+11=23$

Thus

$FD^2=12^2+23^2=673$

Solving

$FD=\sqrt{673}$

$\boxed{FC=25.9}$