If G is centroid of ABC, then (GA^2 + GB^2 + GC^2): (AB^2 + BC^2 + CA^2) is equal to

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If G is centroid of $\Delta$ ABC, then (GA^2 + GB^2 + GC^2):
(AB^2 + BC^2 + CA^2) is equal to

Show answer and solution

GA^2 + GB^2 + GC^2 =

\frac{1}{9}

(2b^2 + 2c^2 - a^2) +

\frac{1}{9}

(2a^2 + 2c^2 - b^2) +

\frac{1}{9}

(2a^2 + 2b^2 -
c^2 ) =

\frac{1}{3}

(a^2 + b^2 + c^2)

Source: Grass-G / M-24 Mathematics Paper 31 Dec.docx

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