Question

in the given figure ABC is a right angled triangle qt C .if D is mid point of BC , prove that AB^2=4AD^2-3AC^2

Answer 1

Now,
ABC is an right angled triangle right at c
therefore, d is mid point. so, bd=dc.
now, ab^2=bc^2+ac^2 by Pythagoras theorem
=(2dc)^2+ac^2
=[4(ad^2-ac^2)]+ac^2
=4ad^2-4ac^2+ac^2
ab^2=4ad^2-3ac^2
proved