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Question

ABCD is a quadrilateral. E is the point of intersection of the line joining the midpoint of the opposite sides. If O is any point and OA+OB+OC+OD=xOE, then x is equal to


Your Answer
A
3
Your Answer
B
9
Your Answer
C
7
Correct Answer
D
4

Solution

The correct option is D 4
Let
OA=a, OB=b, OC=c and OD=d

Therefore,
OA+OB+OC+OD=a+b+c+d
Let P, is the midpoint of AB,
=a+b2 
Let Q, is the midpoint of CD,
=c+d2
Therefore, the midpoint of PQ is a+b+c+d4

Similarly, the midpoint of RS is a+b+c+d4
OE=a+b+c+d4
x=4

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