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If G is an interior point of triangle ABC and GA+GB+GC=0, prove G is the centroid of the triangle ABC.

If G is an interior point of triangle ABC and GA+GB+GC=0, prove G is the centroid of the triangle ABC.

Grade:12

1 Answers

Vikas TU
14149 Points
5 years ago
Dear Student,

Given: GA+GB+GC=0
=>-GA+GM+GC=0
=>2GD=AG=GB+GC
=>2GD=GB+GC
=>GD=(GB+GC)/2
so in triangle GBC, GD will be the median
similarly, we can prove for triangles GAB and GAC.
so G is the centroid of the triangle i.e. mid point of all medians. (proved)
 
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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