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A B C D are four points in a plane an...

`A B C D` are four points in a plane and `Q` is the point of intersection of the lines joining the mid-points of `A B` and `C D ; B C` and `A Ddot` Show that ` vec P A+ vec P B+ vec P C+ vec P D=4 vec P Q ,` where `P` is any point.

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