Question

D,E,F are the mid points of BC, CA and AB of triangle ABC and BE intersect in G, then AG + BG + CG is equal to ?​

Answer 1

Answer:

D, E, F are mid points of BC, CA AB of △ABC. If AD and BE intersect in G, then AG + BG + CG is equal to. Description for Correct answer: Here G is the centroid.

Answer 2

Since D, E and F and the mid points of BC, CA and AB respectively; AD, BE and CF are the medians of triangle ABC. G is the centroid of triangle ABC.

Therefore, G divides AD, BE and CF in the ratio 2 : 1, i.e., AG : GD = 2 : 1, BG : GE = 2 : 1

=> AG = 1/3 AD, BG = 1/3 BE, CG = 1/3 CF

=> AG + BG + CG = 1/3(AB + BE + CF).

Therefore, AG + BG + CG = 1/3(AB + BE + CF).