G is the centroid of triangle ABC . if AG =BC then
angle BGC is ?

• Ans: 90 degree
  
  Solution: It would be easy if I could draw the diagram, but its difficult here. But I am trying my best to explain it.... :)
  
  Centroid cuts the median as 2:1
  So, say the median from A cuts the side BC at point at X, then GX= half of AG
  
  now BC= AG, so, GX=BX=CX.
  and the angle of GXB=GXC=90 degree.
  
  So, the angle of BGX=45 and angle of CGX=45
  
  So, the angle of BGC= 90 degree.
  
  Pls reply if I am wrong....
• 9 years agoHelpfull: Yes(53) No(5)
• 90 deg
  
  Soln. Let median from A on side BC via centroid G cuts BC on D, i.e. BD=CD=(1/2)BC.
  Since AG:GD=2:1, so GD=(1/2)AG=(1/2)BC as BC=AG given
  So, we can say that GD=BD=CD, i.e. tr(GDC) & tr(BGD) are isosceles.
  Therefore, ang(GBC)=ang(BGD)=x(say) and ang(GCB)=ang(CGD)=y(say)
  Value of angle BGC is reqd, i.e. x+y.
  In tr(BGC), ang(GBC)+ang(BGC)+ang(GCB)=180
  i.e x+(x+y)+y=180
  2x+2y=180
  x+y=90=reqd angle BGC
• 9 years agoHelpfull: Yes(26) No(2)
• 90 deg
  
  Soln. Let median from A on side BC via centroid G cuts BC on D, i.e. BD=CD=(1/2)AD.
  Since AG:GD=2:1, so GD=(1/2)AG=(1/2)
  
• 9 years agoHelpfull: Yes(0) No(2)
• 90 degree is the right answer
• 9 years agoHelpfull: Yes(0) No(0)
• 90 dergree is a ryt answer
• 9 years agoHelpfull: Yes(0) No(2)
• soumen maity..how is the angle GXB=GXC=90??
• 7 years agoHelpfull: Yes(0) No(0)
• Property of centroid G
  AG = 2GM
  
  as AG = BC for the given condition
  2GM = BC (where M is the midpoint of BC)
  
  thus BM = MG = MC
  
  angles MGB and GBM are equal
  angle MGC and GCM too
  
  so MGB + MGC = GBM + GCM
  that is
  BGC = GBM + GCM
  
  As the sum of all three angles is 180°
  angle BGC is 90° and GBM + GCM = 90
• 7 years agoHelpfull: Yes(0) No(0)