Given triangle ABC the point J is the center of the excircle 
opposite the vertex A. This excircle is tangent to side BC at M , and to lines AB and AC at 
K and L, respectively. Lines LM and BJ meet at F , and lines KM and CJ meet at G. Let 
S be the point of intersection of lines AF and BC, and let T be the point of intersection of 
lines AG and BC. Prove that M is the midpoint of ST