If in a `Delta ABC`, O and `O'` are the incentre and orthocentre respectively, then `(O' A+O'B +O'C)` is equal to

Options

A. O' O
B. O O '
C. 20'0
D. O

Answer

D

Explanation

Let G be the centroid of Delta ABC. Then, O', G, O are collinear and G divides O' O in the ratio 2 : 1` I, e, (O' G)/ (OG) = 2/1 `
Now, we have
` OA+OB + OC = 3OG
`
`implies OA+ OB + OC = 2OG + OG`
`implies OA + OB + OC = GO + OG " "[ :' 2OG =GO ]`
`implies OA +OB+OC=OO'`