Answer:
27
Step-by-step explanation:
FE is tangent to the circle with center D at point E and DE is radius.
[tex] \therefore FE \perp DE \implies m\angle FED = 90\degree [/tex]
DE = x
DF = x + 18
FE = 36
By Pythagoras theorem:
[tex] DF^2 = DE^2 + FE^2 [/tex]
[tex] (x+18)^2 = x^2 + 36^2 [/tex]
[tex] x^2 + 36x + 324= x^2 + 1296[/tex]
[tex] 36x + 324= 1296[/tex]
[tex] 36x = 1296-324[/tex]
[tex] 36x = 972[/tex]
[tex] x = \frac{972}{36}[/tex]
[tex] x =27[/tex]
