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In a triangle ABC , If 'O' is the circumcentre and 'H' is the orthocentre, then show that 1) OA + OB + OC = OH & 2) HA+HB+HC =2HO. 🤔🤔🤔

In a triangle ABC , If 'O' is the circumcentre and 'H' is the orthocentre,  then show that 
1) OA + OB + OC = OH 
& 2) HA+HB+HC =2HO.
🤔🤔🤔

Grade:11

1 Answers

Arun
25763 Points
2 years ago
we know that O'G =2GO  where G is the centroid of trianglelet a point D between B and CSo, OD =(OB+OC )/2now OA + OB + OC = OA + 2ODwe know that G devide the point A and mib point of apposite side(D) in ratiio  2:1So, OG =(OA 2OD)/(2+1)So, OA + OB + OC =3OG=2OG + OG=GO'+OG =OO'

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