If G be the centroid of a triangle ABC, prove that,  `AB^2+BC^2+CA^2=3(GA^2+GB^2+GC^2)`

G is the centroid of a triangle ABC, show that : vec(GA)+vec(GB)+vec(GC)=vec0 .

If G is the centroid of triangle ABC , prove that area triangle AGB = 1/3 area triangle ABC .

In any triangle ABC, prove that cos A= frac{b^2+c^2-a^2}{2bc} .

In any triangle ABC, prove that : (tanC)/(tanA)= (b^2+c^2-a^2)/(a^2+b^2-c^2) .

In any triangle ABC, prove that : b^2 sin 2C + c^2 sin 2B = 2 bc sin A .

If A, B, C are interior angles of triangle ABC, prove that :- cos^2(A/2)+cos^2((B+C)/2)=1 .

In fig., AD is a median of a triangle ABC and AM bot BC.Prove that :- AC^2+AB^2= 2AD^2+1/2BC^2 . .

In figure, AD is a median of a triangle ABC and AM bot BC. Prove that AC ^(2) + AB ^(2) = 2 AD ^(2) + (1)/(2) BC ^(2).

In figure, AD is a median of a triangle ABC and AM bot BC. Prove that AB ^(2) = AD ^(2)- BC. DM + ((BC)/( 2 )) ^(2)

In any triangle ABC, prove that AB^2 + AC^2 = 2(AD^2 + BD^2) , where D is the midpoint of BC.