Let ABC be a triangle with incircle k. Let D, E and F be the points of tangency of k with AB, BC and CA. Let G be the intersection of DF and BC and H be the intersection of DE and AC (G, H, E and F are on the same side of AB). Let M be the midpoint of FH and N be the midpoint of EG.
If the area of ABMN is 100 and the area of CMN is 4, find the area of EFGH.
Can you generalize this>