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If in a Delta ABC, O and O' are the ince...

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

A

`2O' O`

B

`O' O`

C

`OO'`

D

`2 OO'`

Text Solution

Verified by Experts

The correct Answer is:
A
Here, `O'A =O'O+OA,`
`O'B=O'O+OB and O'C =O'O +OC`

`therefore O'A+O'B+O'C=3O'O+(OA+OB+OC)" "…(i)`
`because OA+OB+OC=O O' =-O'O`
`therefore O'A+O'B+O'C =3O'O-O'O` [from Eq.(i)]
`implies O'A+O'B+O'C=2O'O`
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