Question

in ABC prove that AB2+AC2=2(AD2+BD2), Where D is the middle point of BC. solve by coordinate method

Answer 1

Firstly, this is known as the Apollonius' theorem.

Let A(0,0), B(a,0) and C(c,d) and so D({a+c}/2,d/2)

Now use distance formula and put values and you'll get AB²+AC²=2(AD²+BD)²