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 \(\displaystyle 11S/24\), where S is the area of the triangle ABC.

2. Let ABC be a triangle such that angle ACB = 135°. Prove that:

\(\displaystyle AB^2=AC^2+BC^2+\sqrt{2}\timesAC\timesBC\)

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