If o is the circumcenter, G is the centroid and O' is orthocenter or triangle ABC then prove that:

Options

A. `vec(O'O)`
B. `vec(O O')`
C. `2vec(O O')`
D. `2vec(O' O)`

Answer

C

Explanation

Replacing S by O in illustration 2, we get
`O'vec(A)+O'vec(B) + O'vec(C)=3O' vec(G)`
`rArr O'vec(A) + O'vec(B)+O'vec(C)=2O'vec(G)+O'vec(G)`
`rArr O' vec(A) + O'vec(B) + O' vec(C) = 2O' vec(G)+2G vec(O) " "[ because 2O'G=2GO]`
`rArr O' vec(A) +O' vec(B) + O' vec(C) = 2O' vec(O)`