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

If D is the middle point of the side BC of the triangle ABC, prove that AB^2 + AC^2 = 2(AD^2 + DC^2) .

In Delta ABC, AD_|_ BC . Prove that AB^(2) - BD^(2) =AC^(2) -CD^(2)

In triangle ABC ,if AB=sqrt(2),AC=sqrt(20) ,B=(3,2,0),C=(0,1,4) and D is the midpoint of BC then AD=

In a Delta ABC , angleB is an acute-angle and AD bot BC Prove that : (i) AC^(2) = AB^(2) + BC^(2) - 2 BC xx BD (ii) AB^(2) + CD^(2) = AC^(2) + BD^(2)

In triangle ABC , seg AD_|_side BC , B-D-C. Prove that AB^2+CD^2=BD^2+AC^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 an equilateral triangle ABC, AD _|_ BC . Prove that : AB^(2) + CD^(2) = 5/4 AC^(2)

In a Delta ABC, /_ B is an acute-angle and AD bot BC . Prove that: AB^2 + CD^2 = AC^2 + BD^2