The Problem: A line $AB$ has length $2a$. With $C$ being its midpoint, a perpendicular $DC$ of length $b$ is dropped on $AB$ from above. Now, let $E$ be the point to the left of $D$ on a line parallel to $AB$ and containing the point $D$, such that $DE$ has the length $c$. Points $G$ and $N$ are chosen on lines $EA$ and $EB$ respectively in such way that angles $EGC$ and $ENC$ are equal. Find the coordinates of points $G$ and $N$ if $C$ has the coordinates $(0,0)$ and $AB$ is on the X-axis.
It's pretty simple to find out the following coordinates: $A(-a,0)$, $B(a,0)$, $D(0,b)$, $E(-c,b)$. Going from there, I feel like using the angle equality by equating cosines of equal angles between vectors $GE$ and $GC$ and $NE$ and $NC$ respectively. I am stuck here because of two many unknown factors, even though such angle is unique per each unique lengths $a$, $b$, $c$.
