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 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.

In any triangle ABC, prove that AB^2 + AC^2 = 2(AD^2 + BD^2) , where D is the midpoint of BC.

In a triangle ABC, B=90^@ and D is the mid-oint of BC then prove that AC^2=AD^2+3 CD^2

In the given figure, triangle ABC is a right triangle with angleB=90^(@) and D is mid-point of side BC. Prove that : AC^(2)=AD^(2)+3CD^(2)

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 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 .

In a triangle ABC , AB = 2, BC =4 ,CA = 3 . If D is the mid-point of BC, then the correct statement(s) is/are

The given figure shows a triangle ABC, in which AB gt AC . E is the mid-point of BC and AD is perpendicular to BC. Prove that AB^(2)- AC^(2)= 2BCxxED .

In triangle ABC, the line joining the circumcenter and incenter is parallel to side BC, then cosA+cosC is equal to -1 (b) 1 (c) -2 (d) 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) .