Question

Find x. Assume that segments that appear tangent are tangent.

Answer 1

Answer:

27

Step-by-step explanation:

FE is tangent to the circle with center D at point E and DE is radius.

$\therefore FE \perp DE \implies m\angle FED = 90\degree$

DE = x

DF = x + 18

FE = 36

By Pythagoras theorem:

$DF^2 = DE^2 + FE^2$

$(x+18)^2 = x^2 + 36^2$

$x^2 + 36x + 324= x^2 + 1296$

$36x + 324= 1296$

$36x = 1296-324$

$36x = 972$

$x = \frac{972}{36}$

$x =27$