I assumed both EG and EF are tangents of the circle. Therefore :
[tex]\boxed{ \boxed {\overline {EG} = \overline {EF} }}[/tex]
Equate EG and EF:
[tex]5x = \dfrac{x^2}{2} [/tex]
Multiply by 2 on both sides:
[tex]x^2 = 10x[/tex]
Subtract 10x from both sides:
[tex]x^2 - 10x = 0[/tex]
Take x out as the common factor:
[tex]x(x - 10) = 0[/tex]
Apply zero product property:
[tex]x = 0 \text { or }x = 10[/tex]
Since x cannot be 0, therefore x is 10.
[tex]\text {EF } = \dfrac{x^2}{2} = \dfrac{10^2}{2} = \dfrac{100}{2} = 50 \text { ft}[/tex]
[tex]\boxed { \boxed { \text {Answer: EF = 50 feet}}}[/tex]
