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 right-angled triangle ABC in which /_C=90^(@), if D is the mid-point of BC, prove that AB^(2)=4AD^(2)-3AC^(2)

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) .

In triangle ABC , angle C = angle 90 D is the mid point of BC, prove that AB^2 = 4AD^2-3AC^2 .

In triangle ABC , angle C = angle 90 , D is the mid point of BC, Prove that AB^2 = 4AD^2 -3AC^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

A B C is a right angled triangle in which /_A=90^0a n d\ A B=A Cdot Find /_B\ a n d\ /_C

A B C is a right-angled triangle is which /_A=90^0a n d\ A B=A Cdot Find /_B\ a n d\ /_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 (ii) A B^2+A C^2=2\ A D^2+1/2B C^2

A B C is a triangle in which A B=A C and D is any point in B C . Prove that A B^2-A D^2=B D C D .

If D is the mid-point of the hypotenuse A C of a right triangle A B C , prove that B D=1/2A C . GIVEN : A A B C in which /_B=90^0 and D is the mid-point of A Cdot TO PROVE : B D=1/2A C CONSTRUCTION Produce B D to E so that B D=D Edot Join E Cdot