If in a triangle `A B C ,` the altitude `A M` be the bisector of `/_B A D ,w h e r eD` is the mid point of side `B C` , then prove that `(b^2-c^2)=a^2//2.`

If in a triangle ABC ,the altitude AM be the bisector of /_BAD, where D is the mid point of side BC, then prove that (b^(2)-c^(2))=a^(2)/2

If in a triangle ABC, the altitude AM be the bisector of /_BAD , where D is the mid point of side BC, then prove that (b^2-c^2)= (a^2)/(2) .

If in a triangle ABC, the altitude AM be the bisector of /_BAD , where D is the mid point of side BC, then prove that (b^2-c^2)= (a^2)/(2) .

In triangle A B C , if A D is the bisector of /_A , prove that: (A r e a( A B D))/(A r e a( A C D))=(A B)/(A C)

In a right A B C right-angled at C , if D is the mid-point of B C , prove that B C^2=4\ (A D^2-A C^2) .

If A D is a median of a triangle A B C ,\ then prove that triangles A D B\ a n d\ A D C are equal in area. If G is the mid-point of median A D , prove that a r\ (triangle B G C)=2\a r\ (triangle \ A G C) .

In a triangle A B C ,\ A C > A B , D is the mid-point of B C and A E_|_B C . Prove that: (i) A B^2=A D^2-B C* D E+1/4B C^2

In an equilateral triangle A B C the side B C is trisected at D . Prove that 9\ A D^2=7\ A B^2

In right-angled triangle A B C in which /_C=90^@ , if D is the mid-point of B C , prove that A B^2=4\ A D^2-3\ A C^2 .

D is the mid-point of side B C of triangle A B C and E is the mid-point of B D . If O is the mid-point of A E , prove that a r(triangle B O E)=1/8a r(triangle A B C) .