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If O be the circumcentre and O` be the orthocentre of a triangle ABC then OA+OB+OC=

If O be the circumcentre and O` be the orthocentre of a triangle ABC then OA+OB+OC=

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago
Dear pallavi
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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