The medians BE and CF of a triangle ABC intersect at G. Prove that the area of ∆ GBC = area of the quadrilateral AFGE.
The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line
is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram
into two parts of equal area.
A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F. Prove that ar (ADF) = ar (ABFC)
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then ar (BDE) = 1/4 ar ( ABC).
If P is any point on the median AD of a ∆ ABC, then ar (ABP) ≠ ar (ACP).
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