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 $$\frac{EF}{ED}=k$$

See also:

• Cramer–Castillon problem