If in a triangle ABC, medians from A and B are perpendicular to each other, then show that a²+b²=5c²

let G be centroid ..
dDbe foot of perrendicular from Aand M be foot of perpend from B

so from appolonius theorem
b^2 +c^2 =2(AD^2 +a^2/a)......1
and a^2+c^2=2(BD^2+b^2)...2
since G cuts medions in 2:1 ratio so AG=2/3 AD
and BG=2/3BD
and AG^2+BG^2=c^2
substutuing we get a^2+b^2=5C62

Posted by nitin on 2008-06-16 05:17:08