Here is my thought on the question;
If one has a straight line of length $758$, points $A(0,0)$ and $D(758,0)$ apart. If one constructs a circle of radius $27$ centered at point $A$ and a circle of radius $26.75$ centered at point $D$. Are there two unique points $B(a_1,b_1)$ and $C(a_2,b_2)$, $B$ on the first circle and $C$ on the second circle such that $BC=752$.
We have the following in order, $B$ on the first circle, $C$ on the second circle, the length of $BC$,
$$(a_1-0)^2+(b_1-0)^2=27^2 \\ (a_2-758)^2+(b_2-0)^2=26.75^2 \\ (a_1-a_2)^2+(b_1-b_2)^2=752^2 $$
Three equations are clearly insufficient for four unknowns, I don't know how WolframAlpha got real solutions.
Even if one does find unique solution to the above system, unless $G=A=E$, line $FG$ is not unique.