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Let O be the circumcentre and O' be the orthocentre of triangle ABC prove that OA + OB +OC = OO' in vector

Let O be the circumcentre and O' be the orthocentre of triangle ABC prove that 
OA + OB +OC = OO' in vector

Grade:12

1 Answers

Arun
25750 Points
5 years ago
Dear student
we know that O'G =2GO
where G is the centroid of triangle
let a point D between B and C
So, OD =(OB+OC )/2
now OA + OB + OC = OA + 2OD
we know that G devide the point A and mib point of apposite side(D) in ratiio 2:1
So, OG =(OA 2OD)/(2+1)
So, OA + OB + OC =3OG =2OG + OG =GO'+OG =OO'

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