Answer:
[tex]x=12[/tex]
Step-by-step explanation:
Since the segment EF appears tangent to the circle, we are assuming that it it is actually tangent.
This assumption gives us a right triangle with base [tex]x[/tex] (because it the radius of the circle), a perpendicular of [tex]35[/tex], and a hypotenuse of [tex]x+25[/tex]; therefore, from the Pythagorean theorem we have
[tex]x^2+35^2=(x+25)^2[/tex].
Upon expanding the expression on the right side, we get
[tex]x^2+35^2=x^2+50x+25^2[/tex].
Subtract [tex]x^2[/tex] from both sides:
[tex]35^2=50x+25^2[/tex],
and solve for [tex]x[/tex]
[tex]x=\dfrac{35^2-25^2}{50}[/tex]
[tex]\boxed{x=12}[/tex]
