In triangle ABC, angle B is a right angle. If AC is 6 cm, and D is the mid-point of side AC, the length of BD is:
By Appollonius theorem,
(AB)2 + (BC)2 = 2((AD)2 + (BD)2)
AD = 3 since D is the midpoint of AC
(AC)2 = 2(32 + (BD)2) ....{ (AB)2 + (BC)2 = (AC)2 using Pythagoras theorem }
$\therefore$ 62 = 2(9 + (BD)2)
On solving, we get BD = 3.