Right, I'm gonna give it a go for once, apologies if it's incorrect: Since point D is the midpoint of AC, the length of its altitude to BC is 0.5. Have point P be where the altitude is measured from on BC. Also, have point Q be the same but for A instead. Mainly using Pythagoras' Theorem, we discover: |BD| = √(|BP|² + 0.25) This holds for all triangles. Additionally, |BD|≥0.5, with the equality only occurring when |BP|=0 in an obtuse triangle where |∠ABC|>90°