According to the following picture $E$ is the midpoint of $BD$ and $DC=BD$. If measure of $\angle EGF$ is equals to $90$ degrees then find the value of $\frac {DE} {EF}$.(point A is the center and BC is the diameter.)
My Attempt:if you connect F to B .We have $GF^2=FG×GB$.this is just what I can do. note:only elemenry geometry is allowed.ِ
From the mentioned equality {which should be $GF^2=EG×GB$), get $k = \dfrac {1}{5}$.
Result follows.