Question

10 points

3. Assume that segments that appear to be tangent are tangent. Enter
the number only for your answer. Round answer to nearest tenth.
Find FD.

Answer 1

`FC=25.9`

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=√(673)`

`\boxed{FC=25.9}`