Coordinated Trouble #2

Geometry Level 3

G i s t h e c e n t r o i d O f t h e t r i a n g l e A B C . I f X = G A 2 + G B 2 + G C 2 & Y = C A 2 + A B 2 + B C 2 , F i n d Y X . G\quad is\quad the\quad centroid\quad Of\quad the\quad triangle\quad ABC.\\ If\quad X={ GA }^{ 2 }{ +GB }^{ 2 }{ +GC }^{ 2 }\quad \& \quad Y={ { CA }^{ 2 } }{ +AB }^{ 2 }{ +BC }^{ 2 },\\ Find\quad \frac { Y }{ X } .


The answer is 3.

Soummo Mukherjee by Soummo Mukherjee , 25, India

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1 solution

Shubham Agrawal
Sep 25, 2014

Since it is constant for all triangles take a simple triangle and then proceed Otherwise use vector.

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