Triangle given the centroid G, the line r containing BC, a point N in AC and a point L in AB

1) The line r cuts GL at P and GN at Q.
2) Let L' be the harmonic of G with respect L and P; N' the harmonic of G with respect to N and Q.
3) Let N" be the homothetic of L' with respect to G with ratio -1/2; L" the homothetic of N' with respect to G with ratio -1/2.
4) NN" is the line AC and LL" is the line AB.