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lf G be the centroid of a triangle ABC a...

lf G be the centroid of a triangle ABC and P be any other point in the plane prove that `PA^2+PB^2+PC^2=GA^2+GB^2+GC^2+3GP^2`

Text Solution

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`G ` is intersection of median
`D` is mid[point of DC
`G(0,0)`
Coordinates of D=`((c + e)/2, (d+f)/2)`
centroid of triangle G=`((a+c+e)/3 , (b+d+f)/3)`
`(a+c+e)/3 = 0& (b+d+f)/3 = 0`
`e= -(a+c) & f= - (b+d)`
`PA^2 + PB^2 + PC^2 = GA^2 + GB^2 + GC^3 + 3GP^2`
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