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[*] ABCD is a square with side 1. M is the midpoint of AB, and N is the midpoint of BC. The lines CM and DN meet at I. Find the area of the triangle CIN.
[*] The midpoints of the sides AB, BC, CD, DA of the parallelogram ABCD are M, N, P, Q respectively. Each midpoint is joined to the two vertices not on its side. Show that the area outside the resulting 8-pointed star is $\frac{2}{5}$ the area of the parallelogram.
[*] ABC is a triangle with CA = CB and centroid G. Show that the area of AGB is $\frac{1}{3}$ of the area of ABC.
[*] Is (ii) true for all convex quadrilaterals ABCD? 
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