Given that c is equidistant from the sides of ghi, what can you conclude about point c? find cf if cd = 2x + 4 and ce = 4x. a. c is the incenter of ghi; cf = 2 b. c is the incenter of ghi; cf = 4 c. c is the incenter of ghi; cf = 8 d. c is the circumcenter of ghi; cf = 8

We know that
The incenter can be defined as the point equidistant from the three sides of the triangle. This means a circle can be drawn with the incenter as the center touching the three sides of the triangle.

see the attached figure to better understand the problem

CF=CE=CD
so




therefore
the answer is the option 
C). C is the incenter of GHI; CF = 8