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Prove the cen...

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Prove the centroid their of triangles

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Q. P , Q , R divided the sides of the triangles ABC 1 the same ratio . Prove that the centroids of the triangles ANC and PQR coincide

G

is the centroid of a triangle

A B C

¯ G A + ¯ G B + ¯ G C = 0

Q. Which of the following options have their centroid outside the triangle?

In the figure below, G is the centroid of ΔABC.

Prove that the triangles AGB, AGC, BGC have the same area.

If G be the centroid of a triangle ABC, prove that :

$A B^{2} + B C^{2} + C A^{2} = 3 (G A^{2} + G B^{2} + G C^{2})$

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