[math]R[/math] is the midpoint of [math]BD[/math], [math]S[/math] the midpoint of [math]AC[/math], and [math]T[/math] the midpoint of [math]EF[/math]. [math]RST[/math] are collinear[br]In the diagram above we have [math]U[/math] the midpoint of [math]BC[/math], [math]W[/math] the midpoint of [math]CE[/math] and [math]V[/math] the midpoint of [math]BE[/math].[br][br][br]From this it is evident that [math]UR[/math] and [math]WT[/math] are parallel to [math]c[/math], [math]VR[/math] and [math]WS[/math] are parallel to [math]d[/math], [math]US[/math] and [math]VT[/math] are parallel to [math]a[/math]. The line we choose here doesn't really matter[br][br]Now we have three points on a line and three pairs of parallel lines. Let [math]M[/math] be the intersection of [math]RS[/math] with [math]b[/math]. Suppose that [math]RS[/math] does not pass through [math]T[/math], and call the intersection of [math]RS[/math] with [math]VT[/math] [math]T_1[/math] and [math]WT[/math] [math]T_2[/math]. Then we have [math]\frac{MR}{MT_2}\cdot\frac{MS}{MR}\cdot\frac{MT_1}{MS}=\frac{MU}{MW}\cdot\frac{MW}{MV}\cdot\frac{MV}{MU}=1[/math] which simplifies to [math]MT_1=MT_2[/math] which probably means [math]T_1=T_2=T[/math][br][br]This is probably a special case of something, still haven't learnt any projective geometry sadly