Question
ABCD is a parallelogram. E, F are mid-points of BC, CD respectively. AE, AF meet the diaginal BD at Q, P respectively. Show that PQ trisects DB.
Solution
Take A as origin. Let 
be the position vectors of B, C, D respectively. Let M be the point of intersection of diagonals of AC and BD.
In ∆ADC, P is the centroid as it is the point of intersection of two medians AF and DM as M is midpoint of AC.
∴ P divides BD in the ratio 2 : 1
Similarly Q divides DB in the ratio 2 : 1
Hence the result.
be the position vectors of B, C, D respectively. Let M be the point of intersection of diagonals of AC and BD.In ∆ADC, P is the centroid as it is the point of intersection of two medians AF and DM as M is midpoint of AC.
∴ P divides BD in the ratio 2 : 1
Similarly Q divides DB in the ratio 2 : 1
Hence the result.
