[Cramer–Castillon problem](https://en.wikipedia.org/wiki/Cramer%E2%80%93Castillon_problem) being very difficult problem. Related to the Cramer–Castillon problem configuration, I posed a problem as follows:

> *Let $ABC$ be arbitrary triangle and let three collinear points $E'$, $F'$, $D'$ such that $\frac{E'F'}{E'D'}=k$ where $k$ is positive real number. How can construct points $D$ in the circumcircle of $ \triangle ABC$, $E$ in $AB$, $F$ in $AC$ such that $D, E, F$ are collinear and $\frac{EF}{ED}=k$ ?*

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/gOH5o.png