MathNet 2026 — Part 10 Question 20

In the triangle $A B C$ the angle $B$ is not a right angle, and $A B : B C = k$. Let $M$ be the midpoint of $A C$. The lines symmetric to $B M$ with respect to $A B$ and $B C$ intersect $A C$ at $D$ and $E$. Find $B D : B E$.