I am looking for a construction of my broblem 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 $(ABC)$, $E$ in $AB$, $F$ in $AC$ such that $D, E, F$ are collinear and* $$\frac{EF}{ED}=k$$
[![enter image description here][1]][1]

**See also:**

* [Cramer–Castillon problem](https://en.wikipedia.org/wiki/Cramer%E2%80%93Castillon_problem)


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