Question

If G is the centroid of triangle with vertices `A(a,0),B(-1,0)` and `C(b,c)` then `(AB^(2)+BC^(2)+CA^(2))/(GA^(2)+GB^(2)+GC^(2))=`
A. 1
B. 2
C. 3
D. 4

Answer 1

Correct Answer - C
Vertices are `A(a,0),B(-a,0)` and `C(b,c)`
`:.` Centroid is `G((b)/(3),(c)/(3))`
`(AB^(2)+BC^(2)+CA^(2))/(GA^(2)+GB^(2)+GC^(2))`
`=(4a^(2)+(a+b)^(2)+c^(2)+(a-b)^(2)+c^(2))/(((b)/(3)-a)^(2)+((c)/(3))^(2)+((b)/(3)+a)^(2)+((c)/(3))^(2)+((2b)/(3))^(2)+((2c)/(3))^(2))`
`=(4a^(2)+2c^(2)+2a^(2)+2b^(2))/((2b^(2))/(9)+2a^(2)+(6c^(2))/(9)+(4b^(2))/(9))=3`