Answer:
CD=14
DE=21
Step-by-step explanation:
ΔCDE is similar to ΔFNE (∠E≅∠E, ∠NFE≅∠DCE) by AA similarity
Using Thales' Intercept Theorem Corollary, you know that:
EN/ED=EF/EC=NF/CD=12/20
Let DN be 8x and NE be 12x
Let NF be 12y and CD be 20y
Then you have a system of equations:
20x+20y+20=55
8x=12y
By solving them, you get y=0.7 and x=1.05⇒
DE=21 and CD=14
