Question 40
In an acute triangle $ABC$ we have $|AC| \gt |AB|$. Let $D$ and $E$ be two points on the sides $AC$ and $AB$ such that $|CD| = |BE|$. Denote the intersection of the segments $BD$ and $CE$ by $F$ and let $G$ be a point on the segment $AC$ such that the line $GF$ is parallel to the bisector of the angle $\angle BAC$. Prove that $|CG| = |AB|$.