Question

P is the point of intersection of the diagonals of the parallelogram ABCD. If O is any point, then `overline"OA" + overline"OB" + overline"OC" + overline"OD"` = ______ 

Options

• `overline"OP"`

• 2`overline"OP"`

• 3`overline"OP"`

• 4`overline"OP"`

Answer 1

P is the point of intersection of the diagonals of the parallelogram ABCD. If O is any point, then `overline"OA" + overline"OB" + overline"OC" + overline"OD"` = `underline(4overline"OP")`.

Explanation:

P will be the mid-point of AC and BO.

 

∴ `overline"OA" + overline"OC" = 2overline"OP"` ...........(i)

and `overline"OB" + overline"OD" = 2overline"OP"` ..............(ii)

Adding (i) and (ii), we get

`overline"OA" + overline"OB" + overline"OC" + overline"OD" = 4overline"OP"`