vec(OA) + vec(OB) +vec(OC) is equal to

### Question Asked by a Student from EXXAMM.com Team

Q 2212612530.     Let O, N, G, and O' are the circumcentre, nine point centre, centroid and orthocentre of a Delta ABC respectively. AL and BM are
perpendiculars from A and B on sides BC and CA respectively. Let AD be the median and OD is perpendicular to side BC. Let R
be the circum radius of Delta ABC, then OA = OB = OC = R.

Now, in Delta OBD, OD = R cos A, in Delta ABM, AO' =AM sec (90^(circ) -C) ( :. angle O' AM = 90^(circ) -C )

 = AM cosec C= (C cos A)/(sin C)

= 2 R cos A

 :. AO' =2 OD

If S be any point in the plane of Delta ABC and AP is the diameter of the circum circle.
 vec(OA) + vec(OB) +vec(OC) is equal to
A

vec(OO')

B

2 vec(O'O)

C

2 vec(AO)

D

vec(ON)

#### HINT

(Provided By a Student and Checked/Corrected by EXXAMM.com Team)

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