I'm totally stumped on how to do these:
1. Let P and Q be the points on the sides AB and BC of a tringle ABC respectively such that BP = 3PA and QC = 2BQ. Let K be the midpoint of the segment PQ. Prove that the area of the triangle AKC is equal to , where S is the area of the triangle ABC.
2. Let ABC be a triangle such that angle ACB = 135°. Prove that: