Question

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

Answer 1

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

`2x+4=4x \\4x-2x=4 \\2x=4 \\x=2`


`CF=4x \\CF=4*2=8`

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