Exercise-ABC-is-a-triangle-A-B-C-are-respec-tively-middles-of-sides-BC-AC-and-AB-G-is-isobarycenter-situated-at-equal-distance-of-A-G-and-C-1-By-using-the-theorem-of-medians-

Question Number 94296 by mathocean1 last updated on 17/May/20

Exercise

ABC is a triangle . A^{'}; B^{'}; C^{'} are respec -

tively middles of sides : [BC]; [AC] and [AB] .

G is isobarycenter (situated at equal distance

) of A, G, and C .

1) By using the theorem of medians,

show that :

{GB}^{2} + {GC}^{2} = \frac{1}{2} {GA}^{2} + \frac{1}{2} {BC}^{2}