Let P be an arbitrary point inside the triangle ABC. Let A1,B1 and C1 denote the intersection points of the straight lines AP,BP and CP, respectively, with the sides BC,CA and AB. We order the areas of the triangles AB1C1,A1BC1,A1B1C. Denote the smaller by S1, the middle by S2, and the larger by S3. Prove that S1S2≤S≤S2S3 ,where S is the area of the triangle A1B1S1. geometryarea of a triangleareasgeometric inequalitytriangle inequalityinequalities