Question

In triangle abc, if 'O' is the circumcentre and H is the orthocentre, then show that OA+OB+OC=OH

Answer 1

we know that

HG=2GO where G is centroid of triangle

let a point D, between B and C

OD=(OB+OC)/2

OA+OB+OC=OA+2OD

we know that G divide The point A and midpoint

opposite side in ratio 2 :1

OG=

3

OA+2OD

OA+OB+OC=30G=20G+OG

=HG+OG

OA+OB+OC=HO

Hope it's help to you