Question

In triangle abc if ad is a median then AB2 +AC2 =2(AD2+BD2)

Answer 1

In triangle ABD
By using pythagorous theorem,
AB^2 = AD^2 +BD^2 -1

In triangle ADC
By using pythagorous theorem,
AC^2 = AD^2 +DC^2. -2

add 1 and 2
AB^2 +AC^2 = AD^2 +BD^2 +AD^2 +DC^2
AB^2 +AC^2 = 2AD^2 +BD^2 +BD^2. (AD is a median)
AB^2 +AC^2 =2AD^2 +2BD^2
Proved.