Question
ABCD is a quadrilateral and O is any point in its plane. Show that it 
then O is the point of intersection of lines joining the middle points of the opposite sides of ABCD.![]()
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Solution
Let E. F, G, H be mid-points of the sides AB. BC. CD. DA respectively of quadrilateral ABCD.
∴ EFGH is a || gm [From Co-ordinate Geometry]
∴ diagonals EG and FH bisect each other at P (say)
Now, 
∴ O coincides with P which is the point of intersection of lines joining the middle points of the opposite sides of ABCD.
