If $A B C D$ be parallelogram and $P$ be the midpoint of the intersection of the diagonals. if $O$ is any point, then $O A + O B + O C + O D$ is?

$3 O P$

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$4 O P$

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$2 O P$

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$\frac{1}{2} O P$

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Solution

The correct option is B
$4 O P$

Explanation for the correct options:
Finding the value for $O A plus O B plus O C plus O D space$ :
Given, $A B C D$ be parallelogram and $M$ be the midpoint of the intersection of the diagonals.
Step2. Finding the value of $O A plus O B plus O C plus O D space$ :
Now
$\begin{array}{rcl} O A + O B + O C + O D & = & (O P + P A) + (O P + P B) + (O P + P C) + (O P + P D) \\ = & 4 O P + (P A + P B + P C + P D) \\ = & 4 O P + (P A - P A + P B - P B) \\ = & 4 O P \end{array}$
For parallelogram $P$ bisects the two diagonal.

Hence, correct option is $(B)$

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O \vec{A} + O \vec{B} + O \vec{C} + O \vec{D} =

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A B C D

- - \to O A + - - \to O B + - - \to O C + - - \to O D

- - \to O A + - - \to O B + - - \to O C + - - \to O D

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