Given a triangle $ABC$, $BC = 2 \cdot AC$. Point $M$ is the midpoint of side $ BC$ and point $D$ lies on $AB$, with $AD = 2 \cdot BD$. Prove that the lines $AM$ and $MD$ are perpendicular.
Problem
Source: 2023 Czech-Polish-Slovak Match Junior, individual p1 CPSJ
Tags: perpendicular, geometry
