Problem (2008CHNSouthEastMOp6): Circle $I$ is the incircle of $\triangle ABC$. Circle $I$ is tangent to sides $BC$ and $AC$ at $M,N$ respectively. $E,F$ are midpoints of sides $AB$ and $AC$ respectively. Lines $EF, BI$ intersect at $D$. Show that $M,N,D$ are collinear.
AlphaGeometry formalization: a b c = triangle; i = incenter a b c; m = foot i b c; n = foot i a c; e = midpoint a b; f = midpoint a c; d = on_line e f, on_line b i ? coll m n d
HAGeo formalization: A B C = triangle; I = incenter A B C; BC = line B C; M = foot I BC; AC = line A C; N = foot I AC; E = midpoint A B; F = midpoint A C; EF = line E F; BI = line B I; D = intersection EF BI; Prove: collinear M N D
Difficulty score: 1.6