I'm relying only on the geometry I learned in high school.
Given a scalene obtuse triangle $ABC$, where $AC$ is opposite the obtuse angle, and a point $D$ in $AC$ such that $AD = DC$ (a midpoint).
Then, construct line segment $BD$, subdividing the triangle. What I'm wondering about is whether the length of $BD$ is always, never, or only sometimes the same as the lengths $AD$? Are there any characteristics predictable about the subdivided triangles $ADB$ and $CDB$?