The diagonals of a plane quadrilateral ABCD intersect at O, and X,Y are the mid points of the diagonals AC and BD respectively. Show that:

(vectors)
(i) 2AB + 2BC + 2CA = O
and (ii) If OA + OB + OC + OD = 4OM, find the location of M

Question

The diagonals of a plane quadrilateral ABCD intersect at O, and X,Y are the mid points of the diagonals AC and BD respectively. Show that:

(vectors) 
(i) 2AB + 2BC + 2CA = O
and (ii) If OA + OB + OC + OD = 4OM, find the location of M

anonymous · Answer

Now (i) doesn't look right to me as O is not a vector? Any one shed any light on this

anonymous · Answer

1) I think it is not O but 0 (zero) ABC form a triangle hence AC = AB + BC (vector addition). Hence AB +BC+CA = 0

anonymous · Answer

yes i think you're right, its def a typo in the book

anonymous · Answer

the last part turns out to be mid XY not sure how to prove that?
I'll post the question again...